7 Card Stud Poker is played by 3 - 10 players. Players are dealt two cards face down and one face up and there is a round of betting. Cards 4, 5 and six are then dealt face up with betting on each round. The final card is dealt face down and there is another round of betting before the showdown. 7 Card Stud Poker is still a popular game and is probably second at the moment to Texas Holdem. 

Caribbean Poker is one of the poker games played in a casino between the player and the dealer. Each gets five cards and the player has to decide whether his card is worth betting on after seeing the dealer's first card.
If the player has a better hand than the dealer he is paid out in a fixed odds system depending on the strength of his hand.
The fixed odds range from evens for a pair or high card to 100-1 for a royal flush.

Texas Holdem is by far the most popular poker game in the world today, probably because it is very simple to learn but extremely difficult to master. Two cards are dealt to each player, then three face up on the table (the flop), another face up on the table (the turn), then a final card face up on the table known as the river.

5 Card Draw Poker is played by 3 - 7 players. Each is dealt five cards and there is a round of betting based on the hands. After the betting players can now put up to three cards back in exchange for new ones. (There's one exception where a player can exchange four cards if he shows the fifth to be an ace).
There's a further round of betting and the best hand wins. Draw poker was once the standard way to play but it has of course been overtaken by Texas Holdem.