A genre of video game that is essentially an electronic Collectible Card Game. It may be an exact conversion of a real-world game, or it may be something entirely new. If it's a new game, there will probably be rules and game mechanics that wouldn't be possible in a real-world game. If the game has a plot, of course, you can expect the card game to be Serious Business, maybe even not being considered a "game" despite the obvious rules workings.
To simulate real Collectible Card Games, you'll have to get cards randomly rather than choosing the ones you want (though in real life, you can usually find single cards in game stores), either by receiving them after battles or by buying booster packs at an in-game shop.
A Sister Trope to Fight Like A Card Player.
Magic The Gathering adaptations, the best of which is probably Micropose's one, set on Shandalar and tying up some lose ends from the storyline.
Magic Online is a direct simulation of the tabletop game, to the end that the client is actually free, and you have to buy digital cards through the game just as you would buy physical cards to play normally. Furthermore, if you complete a set of digital cards, you can exchange them with Wizards for a physical copy of that set.
Duels of the Planeswalkers (and the current version, Duels... 2012) is a more limited simulation; the full ruleset is supported, but the controls are simplified (for example, available lands are automatically tapped for mana when you cast a spell) and instead of building decks from scratch, you use one of several preconstructed decks, for which you can unlock additional cards to add to (in the original) or swap in (in 2012).
Yu-Gi-Oh! has some different kinds. Some of them, including the earliest examples like Dark Duel Stories and Forbidden Memories, don't use the real-world card game's rules, while most of the recent ones are faithful to the real game.
Yu-Gi-Oh! has two main series. There World Championship Tournament, which comes out yearly and includes at least one mode with no special gimmicks (as the name implies, it is used for the video game component of the official tournaments). To a lesser extent, there's also Tag Force, which focuses on Tag Team matches.
Xenosaga had a complete card game called "Xeno Card" as a minigame. Unlike other role playing game card games (such as Triple Triad and Tetra Master), Xeno Card was a complete Card Battle Game, complete with boosters, rarity, card types, stack rules, phases, and such.
UltimateMarvel vs. Capcom 3 has a new mode called "Heroes and Heralds" in which there are multiple collectible cards that can be used in normal gameplay; they add many kinds of Status Buff such as speed boost, super armor, new combo strings, and many more.
7th Legion, a 1997 RTS that uses cards to boost units.