Texas Hold'em: The most popular and famous of the "community card" poker games, so-called because each player is dealt two cards face-down, and uses those two in conjunction with five shared community cards (dealt face-up over the course of the hand and shared by all players) to make the best five-card hand. How to play Texas Hold'em.
Omaha: Similar to (and a variation of) Texas Hold'em. Also a community-card poker game, except unlike Texas Hold'em, each player is dealt four cards face-down, and may use any two of those in conjunction with the five shared community cards to make the best five-card hand. Due to the fact that each player has four pocket cards, the permutation of possible hands is greater, and thus it is more difficult to deduce an opponent's hand.
Five Card Stud: Traditional variant of poker (and perhaps one of the oldest) where each player is dealt a combination of five face-down and face up cards over the course of the hand. Usually, the first card is face-down, and the rest of the cards are dealt face-up. The winner is the player with the best five-card hand.
Seven Card Stud: Once the most common form of home and casino poker, before the surge in popularity of Texas Hold'em. Similar to Five Card Stud, except over the course of the hand, each player is dealt two cards face-down, then four cards face-up, then a final card face-down. Again, the winner is determined by which player can make the best five-card hand from the cards received.