There are many different kinds of poker. Below some basic poker variations.

Chinese Poker (also referred to as Russian Poker)
A 52-card deck is used and 13 cards are dealt to 4 players each. Each player arranges the 13 cards into their 3 best poker hands known as the "Front", "Middle", and "Back". The "Front" is a 3-card hand. Both "Middle" and "Back" are 5-card hands and must outrank the "Front" (3-card hand). If you're playing with a surrender option, after the cards have been dealt (and the players have arranged their cards into these 3 hands), then each player elects to either play or surrender. If they surrender, they forfeit 2 chips (or points) to each of the other players. If they play, each player's 3 hands are compared to the other players' hands. Each hand you win picks up 1 chip and the overall winner picks up an extra chip. You can rotate the order of accepting surrenders for each game.

Texas Hold'em
Number of players : 4-7
Initial deal : two cards face-down to each player, and three at the center of the table.
Playing : Play begins by dealing two cards face down to each player; these are known as "hole cards" or "pocket cards". This is followed by a round of betting. Most hold'em games get the betting started with one or two "blind bets" to the left of the dealer. These are forced bets which must be made before seeing one's cards. Play proceeds clockwise from the blinds, with each player free to fold, call the blind bet, or raise. Usually the blinds are "live", meaning that they may raise themselves when the action gets back around to them. Now three cards are dealt face up in the middle of the table; this is called the "flop". A round of betting ensues, with action starting on the first blind, immediately to the dealers left. Another card is dealt face up (the "turn"), followed by another round of betting, again beginning to the dealer's left. Then the final card (the "river") is dealt followed by the final round of betting. In a structured-limit game, the bets on the turn and river are usually double the size of those before and on the flop. The player then tries to make the best five-card hand using the his two down cards and the community cards (the cards at the center of the table).
Hand rankings: standard poker, best five card.

7-card Stud
3 to 5 players can play this poker variation. The initial deal is two cards down and one card up to each player. The first betting round starts with the highest hand showing or for the first round the high card. Then another card is dealt up and another betting round this is repeated until there are four cards face up. Then a final card is dealt down and a final betting round held.

The ranking of the hands are the same as regular poker except to take the five best cards out of the ones you are dealt. Variations on the game is to allow wild cards and a five of a kind. This is personally my favorite kind of poker.

5-card Stud
One of the more popular poker variations. This is played much like 7-card stud only with 5-cards. The intial deal can vary in this game and depends on how your group wants to play. 5 card stud is usually dealt either 2 down, 3 up, or 1 down, 4 up, or 1 down, 3 up, 1 down. Once again it is played exactly like 7-card stud with betting rounds held when each new card is put down. Variations can be the use of wild cards and the rank of hands are the standard one in poker.

Chicago
This game is exactly like 7-card stud except that the high spade in the hole splits the spot. The ranking of the hands are standard poker with the best five cards being used. Wild cards and five of a kind is the variations. I'm not thrilled about this variation because you can have a great hand and still have to split the pot with a goof that got lucky to get the ace of spades.
Indian Poker

Not a true game of poker in the real sense, however this game is a riot to play. 2-10 players can play this game. The initial deal is one card to each player, with a fine (usually $1) and the player is out if he looks at his own card. This is how you play the game: Each player holds his card up so that everyone else can see it. Then starting with the player to the left of the dealer, betting begins.

Once the betting is down with, each player looks at his card and the winner takes his pot. The deal then rotates to the left. The game continues for one deck. This is basically a who has the highest card game, but not knowing what your card is can drive you crazy, especially if there is no limit to the pot. High Card rules in this game Ace high, two Low. This game is fun to play and is the ultimate in bluffing. Try keeping a straight face when your friend continues to raise while he is holding a 2 of clubs.

Lowball
3-7 players. Initial deal is five cards to each player. The game is exactly like five card draw except you are trying to get the worst hand. The rank of the hands are the same as standard version of poker except that the lowest hand wins. This is a good game to break up the monotony of regular poker.