In Yu-Gi-Oh!, there are several cards with super-powerful and game-breaking effects. The catch? They're all some ridiculous rarity to the point that only rich kids would have them. If you do have them, don't expect to use them for long, because (chances are) they'll be banned on the next Forbidden List update.
There are also other cards that are common and have powerful effects... until you read their conditions. Their effects are broken indeed, but compared to the hassle of actually using them makes these cards appear worthless to the extreme.
Finally, there are even the reverse of this: Cards made with DETRIMENTAL effects. These come in two varieties: cards that have a low Level (and thus can be played a lot earlier and easier than a higher level card of similar strength) and with extremely high raw statistics, and cards that only have detrimental effects, with no redeeming qualities whatsoever (one card gives your opponent 3000 lifepoints, and does nothing else). The Former have exceedingly high attack power, but are usually nerfed to the point that playing them required you to keep up an extremely high and almost impossible upkeep, otherwise they will nerf themselves into a weaksauce weak target, or outright destroy themselves just to spite you. For some, even that isn't enough, and they'll not only destroy themselves, but take a good chunk of YOUR lifepoints with them. Why are these cards even used? It's because you need an insane, meticulous combination of other cards. Then their effects are devastating. However, unless you're hardcore about the game, you will likely never hear of the other cards used for the combo (since they're often printed some 3-7 sets apart).
For the most part, though, it isn't that complicated. Skill Drain, which blocks all Monster effects, and any of the high-ATK self-destructers, is a very basic combo, and still pretty powerful. Toss up a Fusilier Dragon, Giant Kozaky, Chainsaw Insect or what-have-you with Skill Drain, and you'll have a high-2000s Level 4 against an effect-less opponent, which basically wins itself.
Also, as far as the one that gives your opponent 3000 Life Points, if you play that card (or two, or three at a time) with the card "Bad Reaction to Simochi", it can potentially destroy your opponent in a turn or two. Not so much Blessed With Suck as broken.
Magic: the Gathering has quite a few cards with this sort of effect. The most obvious of these examples is a card from the Worldwake set: Abyssal Persecutor. It's a 6/6 with flying (can't be blocked by non-flyers) and trample (any overkill damage left over after it's blocked goes through to the defending player) for a mana cost of 4. So it's an awesome card for its cost, but the problem is its other ability: the one that reads "You can't win the game and your opponents can't lose the game." Thus, the only way to win the game after playing the card is to somehow remove it from play.
Another Creature in the same line is the Sky Swallower from the Guildpact expansion. 8/8 flier that costs pittance, it comes with the slight downside of requiring you to give all your other cards in play to your opponent. And it's blue as well, so you'll probably be handing over useful effects rather than black self-destructing cards...
Many black cards are designed with a substantial drawback relative to their power: one of the most common is having them be Cast from Hit Points or require a sacrifice of a creature.
The ability called Shroud - a permanent(creature or otherwise) with it cannot be targeted. It seems like a great bonus at first - things like, say, Lightning Bolt are unable to touch it, rendering a shrouded creature immune to most types of removal. The downside is that it applies to you too; you can't Giant Growth it if you need to.
Also, cards such as Thought Reflection and Mind Unbound let you draw insane amounts of cards each turn... whether you want to or not. If for some reason you're unable to defeat your opponent within several turns of casting them, they'll quickly start getting out of hand and you'll end up burning through your entire deck like candy.
A more weaponized version is Forced Fruition. Drawing cards is good, right? Drawing a card every time you cast a spell is fantastic. Drawing SEVEN cards every time you cast a spell? Not so fantastic.
It's worth noting, however, that such cards tend to be the bread-and-butter of the Johnny player archetype; the player who lives for insane, nobody-saw-that-coming card effects and combos, the player who looks at a card that does nothing or worse something self-destructive and thinks, "how can I win with this?" The two aforementioned cards became the core of a popular deck when people realized that the one who loses the health when it leaves play is the one who controls it at the moment, so in conjunction with Donate the card becomes: "you gain 20 life, then force the opponent to lose 20 life the moment they fail to keep up with a constantly increasing mana cost". You can't even destroy the enchantment to save yourself - the moment it goes, you lose 20 life.