To a certain subset of board game players, dice get this reaction. Not a specific use of them, but dice full stop. A less extreme, and significantly more common, version of this being "dice are fine, the roll and move mechanic isn't."
One reason players of board games object to dice more than players of Tabletop RPGs do is that board gamers are traditionally supposed to roll dice where everyone can see them (thus, no computer dice), and the makers of the games rarely provide a safe place to roll them. "Roll and move" can get ambiguous if your dice have just knocked your piece off the board.
Some board games (Trouble comes to mind) try to get around the wild dice by packing them inside a small plastic dome not much bigger than the dice. You press down to "roll." This has its own problems; you can get a numb palm with a long game of one of these, and the mechanism might malfunction, forcing you to either break it open to get at the dice, or roll dice obtained elsewhere.
Others, like Candy Land and Sorry!, eschew dice for a deck of specially-printed cards. Still random, but for some reason, card randomness is less hated than dice randomness.
Many players also prefer games to be mostly or entirely choice-driven, thus placing an emphasis on skill versus luck. It's quite disconcerting to see a hardcore boardgamer overturn a table and stalk away after winning a game on the luck of a draw.
In Chess, Tournament Play, for many years, the fifty move Draw rule counted. The rule was originally 50 moves without a capture or pawn movement and the game is a draw; note that this was not a Scrappy mechanic. Then it was found that certain positions were winnable in more than fifty moves, so the rules were patched. And then patched again. And then patched again. This changed every few years in the 80s, as more and more computer analysis was applied to chess, and more and more positions were thought winnable in more than 50 moves. Eventually, the result was sufficiently baroque that in 2001 it was decided to just leave it at 50 moves.
In the fourth edition of Warhammer 40,000, Skimmers received a lot of hate because they were excessively hard to kill. The worst offenders were Eldar skimmers equipped with holo fields and spirit stones. Add in how most if not all Eldar players typically run three Falcons (or some other skimmer) with this setup, and you have something that made a lot of people angry. Thankfully, they lost a lot of their power in the fifth edition.
Continuing with that theme, the Tau had a strategy called "Fish of Fury" which was a complete Game Breaker under the 4th Edition skimmer rules. This involved taking two infantry squads with accompanying Hover TankAwesome Personnel Carriers called Devilfish. The Devilfish benefited from the difficulty of killing skimmers and the armor of a light tank. By positioning the skimmers in front of the infantry, the skimmers blocked line-of-sight to the infantry squad, preventing them from being targeted. But in the Tau player's shooting phase, the Tau infantry could fire through the Devilfish representing it using its anti-grav engines to thrust upward and open the line of fire, only to drop back down when it came the enemy's turn to fire. This abuse of a poorly thought through mechanic was widely hated in tournament play.
In the fifth edition, the Annihilate mission generated a huge hatedom from Imperial Guard players because the Guard's Troops rules are incompatible with the kill points rule, making this an extreme example of Failure Is the Only Option. For example, one Troops choice for an IG player is worth as many kill points as any other race's entire army in a 500-point game.
"Yeah, so one kill point for the Devilfish, and one for the Drones." IG players are preaching to a blue choir on that one. There's also the 'nid Biovore when the edition first came out. Every time you fire, your enemy gets a kill point. Fortunately, most of the kill point issues with these armies were resolved through updated books and FAQs.
The 5th edition wound allocation rules have a large hatedom as well because of the large number of Ork (Nob Bikers) and Eldar (Seer Council on Jet Bikes) players that have highly varied load outs on multiwound units so you have to pump out large numbers of wounds to kill a single model because wounds can be placed on individuals rather than inflicting full wound casualties. For example, on a 9-model nob biker unit it takes 10 wounds to kill a single one. Both cases are units that are very hard to kill thanks to special rules and proper equipment. It came to the point where the metagame shifted toward being able kill those units with either a few high-powered shots (which due to a Chunky Salsa Rule could kill regardless of wounds) or just spamming so many shots that they could not save against them all. Armies released later in this addition included options with that metagame in mind, introducing balance problems between those armies who could do this easily and those who could not. The update to 6th Edition changed the ways that wounds are allocated, thus reducing the effectiveness of these kinds of builds.
The "pile in" mechanic from 5th edition's assault rules. Previously, there was a considerable amount of finesse in positioning you miniatures right which could allow a weaker squad to defeat a stronger one if you set up the assault right. Not any more...
The baby rule in the Pokémon TCG generated a lot of flak due to adding yet another variable of luck to an already chance-heavy game. Combine with some of the more powerful cards being baby Pokémon and there's trouble. Eliminated in future sets.
Magic: The Gathering has gotten its share of Scrappy Mechanics over its fifteen years. Some qualify for being confusing (Phasing, Banding, Licids), some for being overpowered (Affinity, "Free," Tempest's implementation of Shadow), some for being time-consuming or otherwise cumbersome (shuffling, Naya's "big matters" theme), and some for being just plain stupid (Radiance).
Infect is a notable case. According to head designer Mark Rosewater, a lot of people like it, but those who hate it really, really hate it. Common complaints include it's too powerful (though this is debatable), it's flavourless (having been implemented mainly as an aggro blitz mechanic which is completely at odds with Phyrexia's "slow and subtle" agenda), it's too insular (since infect cards don't have much place outside of an infect deck and vice versa), and it's pointless (damage being dealt via life loss or via poison counters is still damage, and has the exact same impact on gameplay).
Banding isn't by itself bad; it's when they started having effects that gave or removed banding. One creature is white, and requires green mana to activate its banding, a white ability! And of course there's Tolaria, which removes banding. But there was also may band with other legends, which only let that creature band with other legends that had the "may band with other legends" ability. And it wasted a land play for something that couldn't be tapped for mana! Yes, banding got far too complicated far too quickly.
Banding got phased out (no Magic pun intended) around the time cards started to get printed with reminder text for their abilities in earnest and printed rulebooks in every starter became a thing of the past. Which makes sense because while banding in and of itself wasn't that difficult an ability to apply once you grokked it, it was just complicated enough to explain to make the "reminder text" approach impractical given the limited space in each card's text box. (Creatures becoming less useful in numbers that would justify the use of banding as the number of ways to remove them from play individually or all at once without having to engage in explicit combat soared over time may also have had something to do with it.)
Transform is the new Scrappy Mechanic for Magic, as its cards are the first to have different backings. Said cards need to be able to flip over during play, making them incompatible with sleeves, but also must be sleeved or else count as marked cards (and are thus illegal in tournaments and any casual group with a shred of common sense). The solution is to print placeholder cards that garbage up booster packs, with Transform cards held in a pile off to the side. Since all the Transform cards had to be printed on the placeholder, they are few in number—meaning your opponent has a pretty good idea what deck you're running when he sees you have a pile of Transform cards off to the side.
Rolling to hit in 1st and 2nd edition Advanced Dungeons and Dragons. While the rules generally made it pretty easy to work out what you had to roll to accomplish something in almost any given situation, in almost every other case a low dice roll was a good thing. When rolling to hit, however, players had to roll high. Many people felt that assigning characters a number that was lower the better protected-they were was rather counter-intuitive. Expressing a character's skill in battle as the minimum roll needed to injure a person in full plate with a shield and a high dexterity (as opposed to, say, the minimum roll needed to injure a naked person) was worse, however.
Wordof God (Gary Gygax himself) said that he wished he hadn't included the rather cumbersome weapon type having bonuses against certain AC types (an almost universally ignored mechanic) and that he only included psionics in 1st edition (creatures from previous material didn't have any psionic resistance, allowing psionic characters to run rampant) because a friend talked him into it. 1st edition had a LOT of Scrappy Mechanics. They were just flat ignored most of the time and most DM's made houserules instead.
Favored class/multiclass XP penalty rules from 3rd edition was notable for completely failing at what they were meant to do (the idea was to show the difficulty of maintaining skill sets, but a character that takes 1 level in 20 classes takes no hit under them, while a character that takes 15 levels in one take and 5 in another DOES take a hit) and acting like a straitjacket on customization. Exotic base classes were rarely supported as favored classes, making them harder to use. Humans had no set favored class, whereas everyone else had a single favored class - which meant that the already overpowered humans became even more dominant, except that in some cases, the lack of a single favored class actually imposed a XP penalty another race would avoid. And on top of this, prestige classes — which are generally more powerful than multiclassing anyway — don't take the penalty. Very few groups actually use this rule.
For low level 1E/2E games, level limits for non-human races were utterly irrelevant as a balancing factor. For higher level games, OTOH, they put a giant brick wall in the way of the demihuman races being useful, because suddenly you couldn't gain any more levels. To add insult to injury, the level limits also acted as further straitjackets on character design, since outside of the single favored class for a given race, they were often so low as to be punitive even in a low level game. Thankfully eliminated in 3e and later.
In a similar vein, level adjustments are almost never worth it due to being obscenely overpriced. For example, playing a vampire looks awesome on paper, since you get huge stat bonuses and awesome powers like a healing factor, turning into mist at will, and draining your opponents' life with a touch. Trouble is, that will set you back eight levels in a system where the usual level cap is twenty. The end result is a character that can't cast with a damn, hit the broad side of a barn, or survive blows even the Squishy Wizard could tank.
Savage Species was an entire Scrappy Book of poorly-balanced concepts. It's one book almost no sensible DM will allow.
It has a ritual that lets you sacrifice XP (a level 1 template costs 1000 XP, a level 2 costs 3000, etc) to apply templates to your character. Kobolds are bad enough, but when you factor in that the character can drop from level 6 to level 5 and pick up the Necropolitan, Half-Celestial, and Weretiger templates without much hassle, maintaining balance in a party becomes pretty much impossible.
Grappling in 3rd edition was considered confusing and generally wasn't worth it versus hacking a creature to death. However, the 3rd edition grappling rules were the very soul of clarity compared to the 1st edition unarmed combat (grappling/pummelling/overbearing) rules. It wasn't all that uncommon for the bad guys to kidnap, imprison, or otherwise de-equip the party, only for the DM to suddenly announce that the party found a crate of daggers when one of the players pointed out "So I guess we'll be using the unarmed combat rules?"
While Hit Points are not normally a Scrappy Mechanic even when coupled with the usual Critical Existence Failure when player damage outputs are relatively low compared to enemy HP without specific and highly optimized builds, but the same is not true of enemy damage output relative to your HP. Your options become: bypass the broken mechanic by not doing HP damage, which not all classes can do; limit yourself to one of a select handful of builds, as otherwise the enemies will survive to get a turn and thus kill you; or die.
3.5 featured two kinds of casters: Vancian Magic casters prepare their wide selection of spells in the morning, while spontaneous casters know a small pool of spells that they can cast without preparation. This looks fairly balanced, so of course the designers decided to cripple the latter with how nearly all spontaneous casters advanced. They learned stronger spells when their level was double that of the spell (so a sorcerer learned 3rd-level spells at level 6), while Vancian casters learned at double the spell minus one - so a wizard would be learning that same spell at level 5. To make matters worse, most challenges and Prestige Classes were designed with Vancian casters in mind. This basically meant that spontaneous casters were always at least one level behind the curve, and levels 2 and 3 (since you learned your first-level spells at first and your second-level at fourth) were practically Empty Levels. Result? Vancian casters became Tier Induced Scrappies, and many spontaneous casters started using tricks like White Dragonspawn Loredrake Dragonwrought Kobold just to catch up.
While pretty much everything relating to the laughably underpowered truenamer could land in this trope, special thanks must be given to the Law of Resistance and the Law of Sequence. For the uninitiated: The truenamer uses his abilities, called "utterances," by rolling against 15+double the target's CR. (You may be asking, "Doesn't this mean he gets less effective when he levels up?" Answer: Yes.) The truenamer is a buff-and-debuff centric class, so he wants to use his utterances as much as possible, and he doesn't get a lot. Meet the Law of Resistance, which raises the DC of an utterance by 2 every time you use it. (And yes, this is a nightmare to keep track of!) One major trick the truenamer has to boost his utterances is the ability to "reverse" an utterance; for instance, the reverse of a flight utterance forces a target to the ground; the reverse of a sensory booster gives the target a sensory overload. You're probably thinking of ways to use these effects in tandem... meet the Law of Sequence. If you have an utterance active, you can't use it again as long as it's active. Oh, right, and most utterances are single-target, so if you've got two melee fighters in the party and you want to help one out when he's under pressure but you've already buffed one up, you need to cancel all the buffs on the other guy, then redo all of them onto the one who needs them, only they're harder to use now thanks to the Law of Resistance. Yeah, there's a reason this guy gets picked after the adept in Mage Kickball.
In 4th edition you have a similar problem: player damage output compared to enemy HP is still lower, while enemies don't do much damage either. HP became a Scrappy Mechanic anyways, because you're likely to fall asleep long before the enemy has been ground down by HP damage and there are not any ways of bypassing the snoozefest.
Somewhat addressed by WotC in later books, most notably the Dungeon Master's Guide 2, which officially tweaks the rules for creating elite and solo monsters (in other words, exactly the toughest lumps of HP around) by no longer granting them better-than-average defenses for their type and trimming 20% off the HP totals of high-level solos on top of that. (Solo monsters in particular are generally intended to compensate for their lowered life expectancy under this approach by turning red once bloodied.)
3rd edition's sister product, d20 Modern, had the Wealth system. In theory, this means that instead of nailing down all equipment in terms of absolute cost (which was guaranteed to fall victim of Technology Marches On as the high tech gadgets of 2002 like mobile internet and sub-notebook computers became commonplace by 2009), items have a "Wealth DC," which is the character's Wealth modifier (arrived upon via the player's starting occupation and rank in the Profession skill, then adjusted by some Feats) plus a d20 roll. In theory, this keeps item pricing from ever looking too ridiculous. In practice, it meant that a character's gear was essentially randomized and that characters had to either requisition equipment on the honor system or with the GM present. In the end, most GMs ignored it because telling a player he can't play a sniper because he rolled a 2 on his Wealth check and now can't afford a sniper rifle goes against the spirit of the game.
The trouble was compounded in the way Wealth went up and down. If a product cost less than the player's unmodified check, it could be purchased at essentially no cost. If it was higher than the character's base check modifier, it had to be rolled for—and a success lowered the player's Wealth by 1. Wealth was gained by making Profession checks when leveling up, and could award a 0-4 bonus, depending on how well the roll went. This mean that the system gave a huge advantage to characters created above level one; they could roll to gain wealth during their offscreen levels, then buy equipment after their Wealth check rose to get items essentially for free, instead of losing Wealth to roll for those items at level 1.
The Wealth system was also broken wide open by the D20 Future splatbook. Among the things it added was a futuristic device that, while expensive, granted 1-3 feats of the player's choice to that player. The existence of the "Windfall" feat (+3 to Wealth checks, can be taken any number of times), meant that a character could repeatedly buy versions of the device that contained multiple Windfalls until his Wealth modifier was so high he could buy anything.
For Yu-Gi-Oh! card game players: Missing the Timing. Basically, there are two general types of effects: Mandatory (where you have to activate it, regardless of what else is happening, at the time), and Optional (where you can choose to activate the effect or not). Thing is, rulings dictate that the Optional effect must be the last thing to happen, else it "misses the timing" and doesn't get to activate. This can be anything from activating in the middle of a card chain (and not being the last chain link to resolve), to being used as a cost to activate another card, to being tributed to summon another monster. You cannot believe the amount of otherwise-powerful cards that get thwarted simply because their effects say "you can do X", instead of "you do X".
To explain. If a card says "If", even if the effect is optional, you can use it any time after the event, because it grants the ability from that point on. But if the card says "When" then you are only granted the ability to do the optional effect at that specific time. The problem is that the timing rules can and will block you from activating the effect at that time, because something else needs to resolve first. Because the rules force something else to happen before you can use the effect the opportunity is gone, and you have thus missed the timing. What's so annoying is the name of the rule implies that you could have used the effect, and you missed the chance. However the opposite is usually true. There was no way to prevent the timing form being missed!
Back when the game first began, part of the power of cards like the Trap Hole set (which destroyed monsters on summon) was that you could block a monster from using its effect. However, because they activate when a monster is summoned and only destroy it (rather than actively negating its summon attempt), the monster is technically on the field first (this is the reason why it is impossible to destroy Jinzo, a monster which prevents traps from working for as long it's on the field, on summon with Trap Hole), so for some reason it was decided that the player should be able to use the effect of their monster regardless of whether or not it's about to be destroyed. This can result in some ludicrously powerful optional effects happening at a time when the monster should have been dead and buried, and is extremely annoying.
For the record, that is called Priority. And as of March 19, 2011 (now etched in history as the Exceed Rule Patch), this is now abolished and the Trap Hole cards regain their power of eliminating big threat monsters like Judgment Dragon and Dark Armed Dragon.
To put this into further context: due to the abolition of Priority, some creatures that were once thought irreparably-broken have now been unbanned (though still limited), chief among them is Black Luster Soldier, Envoy of the Beginning. Some fans have called for it's brother card, Chaos Emperor Dragon - Envoy of the End, to be unbanned as well, since the entire reason WHY it was broken was because Priority made its ignition effect nigh-uncounterable; it's still extraordinarily powerful, but arguably no more so (or even LESS so) than Judgment Dragon (since CED destroys itself and your hand, as well).
There's also the "Harpie Rule", which only really affects the titular monsters, but is still fairly annoying. To wit, there are several monsters with effects that change their name to that of another monster, usually while it's face-up on the field. However, most all of the Harpie Lady monsters past the initial 2 don't specify where their effects treat their name as simply "Harpie Lady". As such, Konami has issued the ruling that these monsters are treated as having the name "Harpie Lady" for all intents and purposes, including deck construction. What does that mean? Well, you can only have three copies of a specific monster in your deck at any one time, so with the other Harpie Lady monsters being treated as "Harpie Lady" all the time, instead of being able to have three copies of each one of them, you can only have three of any combination of them (for instance, you can only have either one of the original Harpie Lady and two of Harpie Lady # 1, or two of Cyber Harpie Lady, and one of Harpie Lady # 3, but not three each of Harpie Lady, Cyber Harpie Lady, Harpie Lady # 1, and Harpie Lady # 3). This severely limits the potential of a Harpie Lady deck, even more so when you consider all of the awesome support they have... though that might be whythey were given this treatment. Later Harpie cards wouldn't follow this rule, instead only changing their name to Harpie Lady when on the field or in the graveyard, making it possible to use more of them in the deck.
Exalted had the Reactor/Perfect Spam/Lethality/Paranoia Combat/Overwhelming issue, which was a whole bunch of these. Elaborated: Reactor meant that with relentless stunting and mote regeneration Charms, it was comparatively easy to come out of any given action with more Willpower and motes of Essence than you started. These were then spent to activate "paranoia combos", which were massive experience sinks containing every single No Sell power that could be accessed, including perfect defences. If you didn't activate your paranoia combo, you would die because of a preponderance of unpleasant "bad touch" effects, which would kill you, cut off your arms, turn you into a ferret, or otherwise make your life very difficult, not helped by the low health levels of these titan-killing god-kings, which ensured that even if there weren't any bad-touch effects in the oncoming attack, it would still deal quite a lot of harm if it got through your overpriced armour. Overwhelming damage and Essence Ping ensured that armour was largely unhelpful. Notably, the 2.5 errata tried to kill almost all of these: combos became free, mote regeneration was nerfed in the head, stunt regen was dropped to once per action, Essence ping was killed, Overwhelming became far weaker, and armour got cheaper. More abstractly, some players dislike Charms, believing them to be either annoying, too limiting, or overemphasised, and exactly nobody liked attunement motes in the 2.5 errata, but the lethality/paranoia issue was the most widely complained about and the source of many fixes.
In the same system, the diverging math between character creation points and experience points is regarded as this. Most traits bought up in character creation are paid for at a flat rate, but increase in cost exponentially afterwards when bought with experience points. Sub-optimal point investment in character creation, consequently, can leave a character behind literally the equivalent of hundreds of experience points (in a game where 4 per session is the baseline rate). This has persisted through the first and second editions of the games, and the developers have stated it will continue through the upcoming third edition, because it would be "fake equivalence" to correct it, and because "[they] never really bean-counted with any of [their] characters".
Though not quite as widely maligned, due to having some positive upshots, the Resources system is similarly problematic. The Resources trait gives a simple zero-to-five abstract rating of a character's general wealth, meant to avoid having to do painstaking math or accounting. A character can't buy something that costs more than their Resources rating. Purchases below it are "out of pocket" expenses. A purchase equal to the rating is a significant expense, and lowers the rating by 1. However, this means that characters can purchase "insignificant" things in infinite quantities, characters with Resources 1 literally cannot buy anything at all without bankrupting themselves, and merely buying the same items in a certain order completely changes their impact on your wealth. Ex: At resources 3, buying a resources 3 item, then a resources 2 item, then a resources 1 item would drop you to resources 0. If you bought them in reverse order, despite their prices and your wealth being completely unchanged, you would only drop to resources 2.
Car Wars Confetti Rule: Due to a combination of factors (tournament games at conventions with strict time limits; extremely-low-weight engines; minimally-ablative armor), it became a simple matter to design a duelling car whose armor could not be penetrated easily (if at all) by the weapons of the game, singly or in linked masses. The "solution"? Institute a rule where if a car took damage equal to its mass divided by 50, it was automatically reduced to debris even if its armor was unbreached. Unfortunately, the writer of this rule forgot about Ramming, and specifically the fact that a car which was hit by a Ramplate wound up taking four times as much damage as the rammer (due to a poorly-written Ramplate-damage rule — not only did the target take 2x damage, the rammer took 1/2 damage!). Worse: A ram-car could easily have enough armor and other items to render it impossible to hit, much less damage. End Result: Ram-cars became the vehicle of choice, especially in tournaments; players who brought gun-equipped cars had no chance of winning. Mention of Confetti around gamers who remember this period is a Bad Idea....
The priority system for character generation in Shadowrun effectively forces you to design characters in narrow archetypes. The Build Point system replaced it in Fourth Edition, which was much more open to customization, and the Karma Generation system introduced in Runner's Companion is possibly the most versatile character generation method for the system. The developers reintroduced priority generation for Fifth Edition, "fixing" what was not only not broken, but better in the first place.
The least popular mechanics of 13th Age seem to be the "variable class complexity" and "flexible attacks" rules. For the former, classes are arranged from things like the barbarian (whose most difficult decision is "when do I rage") to the wizard (who can pick all kinds of talents that encourage stunting on the fly, coming up with creative ritual uses for combat spells, and so on); while there isn't a great deal of imbalance, at least not in combat, gamers used to 4th edition Dungeons & Dragons often find barbarians and so on to be comparatively dull, leading to a number of homebrew classes aimed at making more complex barbarians and so on. The latter is a mechanic, used mostly by fighters and bards, where the effects you can use depend upon what your hit roll is - some require an even, some an odd, some a high roll, some an even miss - and some people don't like the lack of tactical control this gives you when you're playing those classes, leading to, again, homebrew classes that fill the same battlefield role but with different mechanics.