Collectible Card Games have their Goddamned Bats, too. Duel Masters, for example, has Pyrofighter Magnus, who comes out of nowhere, gets in a cheap shot, and disappears back to his owner's hand. You can only attack an opponent's monster on your turn, which means you can't kill him. If you have a blocker that can kill him, your opponent probably won't summon him, but he'll show up again once the blocker dies.
Yu-Gi-Oh! also had them in the form of Spirit Reaper/Marshmallon and Treeborn Frog/Sinister Serpent. The first two cannot be destroyed in battle, and have weak enough stats to make them safe from most of the popular monster-destruction cards, while the latter two are easily able to return to your hand/field shortly after being sent to your graveyard, no matter how they're sent there. Fortunately for players, Spirit Reaper dies the moment an effect targets it, only one Treeborn Frog can be summoned per turn via its effect, and Sinister Serpent is outright banned. Marshmallon had the consolation of being limited to two per deck until September 2012; now it is again subject only to the Rule of Three. There's also Tsukuyomi (a Spirit monster that flips a monster on the field face-down upon summoning, and bounces back to your hand at the end of the turn), and Yata-Garasu, a Game Breaker if there ever was one. With the ability to prevent the opponent from drawing cards normally and the ability to return to its owner's hand due to it being a Spirit-type, it was essentially an "I win" card that still causes eye twitches when mentioned around seasoned Yu-Gi-Oh! players. Yata-Garasu was actually partly responsible for the Forbidden/Limited List's creation, and is banned, probably indefinitely. Tsukuyomi was likewise...until September 2012, when it's been limited to one per deck. And that's more than enough.
The likely Ur Example in the CCG world is Magic: The Gathering's protection from color ability, which can be bad if you happen to be using the colors protected from. There are auras and equipment to grant creatures protection, as well.
Hypnotic Specter makes your opponent discard a card every time it damages him/her. Said Specter has flying, making it hard to block.
Stinkweed Imp is the ultimate Goddamned Bat of Magic: The Gathering. Weak p/t-wise, but an evasive little sonofagun that'll kill whatever it touches. Oh, and did I mention it comes back from the dead while accelerating the opponent's plan?
Also, blue decks chock full of cheap counterspells. On their own, these cards will never make one win (though they do help make one not lose, a good first step :)). To the opponent, they're goddamn bats as every. Single. Fucking. Card they try to play immediately ends in the graveyard.
In a similar vein, any control deck. Combination include Blue Black using forced sacrificing, hand destruction and counterspells and Blue and White includes Counterspells and denial cards. Black and White, while rare, usually ends up completely locking the opponent down, either by denying the opponent from using anything they play, and destroying their hands and creatures. Most of these decks are built to hold out to build up a mana base or accumulate a set of cards for a instant kill combo, meaning that at all other times you, the opponent, is left sitting there waiting until he either runs out of counters and denials, or the combo goes off.
The Star Wars CCG had a similar card- Jar Jar. Besides being The Scrappy, the original Jar Jar could blow up an enemy with a little luck, but die in the process. A few sets later... Brisky Morning Munchen let you recur him. For a fairly cheep activation price, as far as named characters from the movies go. Throw in a couple of equally annoying cards built around him, and... you get the picture.