Traditional Card Games
Traditional card games are played with a standard 52-card deck, and are usually much older than other card games. Their ranks include Hearts, Go Fish and Chicken in the Barnyard.
Non-Traditional Card Games
Non-traditional card games still use a deck of cards, but not the particular suits and numbers on them. Games like Hat Trick, where you toss cards onto a hat, or House of Cards, where you build structures out of the cards themselves qualify as non-traditional card games.
Non-Collectible Card Games
Non-collectible card games use a single deck unique to that particular game, rather than a 52-card deck. The most popular examples are Uno and Mille Bornes, but there are countless others.
Collectible Card Games
Collectible card games (or trading card games) use thousands of different cards which are sold in blister packs like baseball cards: players build decks using particular combinations of cards, rather than using all of them at once. They include games such as Pokemon, Yu-Gi-Oh! and Magic: the Gathering.
Mixed Card Games
Mixed card games are those where cards are used in conjunction with a board or similar apparatus. Their ranks include games like Talisman and Dungeon! (and they are often grouped as board games).