These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Anticlimax Boss: Diablo himself is painfully easy to defeat. His only ranged attack is a simple blockable instant hit explosion but can be prevented by going melee, he's fairly susceptible to common magic, and has pretty low armor class. Doesn't help that there is an easy way to lure him out without waking his mooks. Excusable because in actuality, the body you're fighting is that of a helpless child.
Chaotic Evil: Hell is depicted this way in the mythos, whose denizens enjoy slaughtering and corrupting mortals and who hold chaos as a cosmic ideal to which all reality should bend. However, besides the Three Prime Evils who rule Hell, most of the forces of Hell seem to in fact be stupid evil, and are perfectly willing to simply slaughter each other for all eternity.
Play the Game, Skip the Story: Who was going to pay attention to it, anyways? If anything, Blizzard knew they shouldn't make anything too original.
Anyone who only played multi-player probably didn't even know there was a story; it skips all the cinematics and most of the background is in the manual.
Complete Monster: Archbishop Lazarus was a prominent figure in both the original Diablo and is mentioned in the first act of Diablo III. He played an integral role in King Leoric's descent into madness and eventual transformation into the Skeleton King, as well as manipulating him into torturing and executing many innocents in the guise of "protecting his kingdom" (up to and including his own queen), feeding Tristram's villagers and the odd adventurer to the demonic Butcher in the first game, and having Albrecht, one of Leoric's two sons, made a vessel for Diablo himself.
The original game had the demon mages at the end of the game, who in addition to teleporting about, hit hard with powerful spells to make even ranged players cringe thinking about taking on groups of them (nevermind the melee players, to which those guys are absolute terrors). They came in swarms, had lightning attacks which could shred your HP down to critical in a few seconds, and teleported away from you before you could do any significant damage. The bane of warriors. It's not unknown to run out of money to spend on healing potions before you run out of enemies to kill.
If those weren't bad enough, they'd often be accompanied by Soul Burners. These winged demonic harlots would NEVER be encountered on their own, and while they weren't able to teleport around like the mages, approaching even an average-sized cluster of them with melee in mind still bordered on suicide for anyone not tooled-up to the eyeballs with special items and healing consumables. Succubi are a close second to the mages, particularly for warriors, as they also tend to come in packs and flood the screen with blood stars. They move at the exact same speed the player does, which makes catching up to them with melee in mind nearly suicidal.
Never mind the triple-immunes on the highest difficulties. These monsters are immune to ALL attacks save physical damage and Stone Curse. The only reliable way to kill them is to lure them out one-at-a-time, stone curse them, then smack them to death with either your own melee attacks or a golem.
Monsters that attack using Blood Star. Due to the game's dearth in providing substantial defense towards the generic "MAGIC"-type damage (ie Bone Spear, Berserk, Blessed Hammer etc) for players, a frequently-encountered stream of blood stars will cause immense grief to characters that don't explicitly load up on hit points and the mod "Magic Damage reduced by [integer]".
Ear Worm: The Tristram town theme from Diablo (or Diablo II, in this case, as it was exactly the same as the version from the first game but with an extra 3 minutes or so of new music added to the end). This theme is so memorable that at the end of Diablo II, after killing Diablo himself, the game plays this theme for five seconds. Every single person who has ever played the first game hears this and shivers at the very sound.
The Sorcerer was ridiculously easy to break by using the MS No-Stun bug. The "stun" that occurs if your character (or a monster) gets hit strongly enough is a huge part of the gameplay. But, Mana Shield can potentially cancel that. The problem is that it works by first applying damage to your life (as usual) but then converting it to your mana. If the damage is greater than your life, you're considered DEAD (and not stunned) for milliseconds until Mana Shield does its work. If your life ends up below your level (which is the stun threshold) you can never be stunned when using Mana Shield. Since sorcerers rely on Mana Shield in the normal gameplay anyway, well... To make it even worse, there's an otherwise feared enemy "Black Death" that when hitting you removes 1 of your maximum life, which you could use.
Unofficial Expansion PackHellfire's easter egg bard was breakable without any bugs because of dual-wield. Just equip a haste/peril weapon combo together with an undead crown or helm or spirits for life-steal. Because peril does 1x WEAPON damage to the user, but 3x CHARACTER damage to the monsters, and such big life-steal will almost always get your HP back, such a combo can potentially cause total havoc.
Literal bats...that teleport. Diablo II adds Flayers, Maggot Young, Flesh Beasts, Leapers and Imps. The Imps teleport. Both games have Fallen/Carvers. Flayers, Fallen, and Carvers all tend to swarm and can be resurrected by their respective Shamans (except for the undead Bone Flayers, which explode for a nasty chunk of damage when they die). Sand Maggots and Flesh Beasts spawn Maggot Young and Flesh Spawn, respectively. Imps are spawned by huts. Leapers move very fast and jump all the time which makes them difficult to kill due more to being hard to click on than having lots of armor or HP.
The first game had a cloning glitch: if you picked up an item off the ground at the exact same time as left-clicking a potion from your belt, the item would appear in your inventory and the potion would be replaced with the same item. Extremely useful for fast cash or online item trades, as rare items sold well, but you could also have duplicate rings (the only item that you were allowed to wear 2 of the same thing).
Could be easily abused to create a level 1 character with maxed stats, as well, as the game included elixirs that each permanently increased a primary stat.
A possible item affix determines if an item increases or decreases the light radius (and thus how far a player can see) around the player character. While the original intention of this stat is that a higher light radius is good and a lower light radius is bad (because stumbling around a darkened dungeon is not exactly the sanest thing to do) to the point that -lr items are considered cursed and a -lr modifier is considered the necessary drawback on several unique items to prevent them from being overpowered... This isn't exactly the case. Light radius is also responsible for determining just how far away monsters in the dungeon activate and begin hunting you down; a higher radius means that more mobs will be out for your blood and a lower radius means you can actually apply some stealth tactics.
Narm: The ending cinematic, depending on which class you played as. When the player character drives Diablo's Soulstone into his/her forehead, the look of pain on the Warrior and Sorcerer's faces is authentic. The Rogue, by contrast, ends up looking like Barbra Streisand.
Overshadowed by Awesome: It's hard to make the Diablo II expansion climactic when the previous game ended with you effectively beating the Devil in Hell.
Play the Game, Skip the Story: The Diablo franchise does in fact have a story, and there are the hardcore "lore-fans" who spend time debating of it, but most players ignore it completely. The franchise also has loads of supplemental materials. Of course, as a result, Blizzard became Genre Savvy enough to know they can get away with Cliché Storm plots (and trailers) and only a few Tropers on this site will actually notice.
Plaguewrath, a frustrating spitter boss. Basically he has a bunch of minions that all act the same way: they spit at nearly double, or even triple the speed of regular spitters, which means that often they'd drop a barrage of deadly spit that can drop you in seconds, before you can do anything. Add the fact that they don't have a melee attack, and unlike regular spitters, will actively run away from you if you try to get close, and you get one frustrating boss. Not to mention that the first time you'll encounter him, Plaguewrath himself takes forever to kill.
Black Death in particular take away 1 hit point permanently on striking (with no indication that this is the case) and can render the game unwinnable if you are playing very badly and get hit hundreds of times, leaving you with a tiny amount of health.
Unless you're a mage who's using Mana Shield... at which point you get to use the ludicrously advantageous "No Stun" bug.
When you die, the save function is disabled, but not immediately. Yes, saving at this point makes the current game unwinnable. It requires timing by the milliseconds, though. A frame too late and the game disables the save function. The easiest way is probably to get a +HP item and then get yourself down to health lower than said item provides you. When you remove the item, you die. If you click and press ESC almost exactly at the same moment, you get to save without having that item on you. No, there is no time to put it back on.
It's possible to make the game unwinnable by abusing the Chamber of Bone entrance in a hilariously stupid way. You need to teleport there before you use the book to open it (either with a scroll of teleport or using a scroll of town portal then going there from town) and leave yourself stuck in a sealed room. Yes, you need to be completely stupid to do this unless you're doing it intentionally for the lulz.