The earliest direct reference to the game Poker shows it's origins in New Orleans around 1830.

Five-card draw poker was once the poker game that everyone and his mother knew how to play. It's the game you'll see in numerous poker scenes in old westerns, the game that many of us first learned, a game to feel nostalgic about. But in recent years, the game has almost vanished. Among the numerous events at the World Series of Poker, there is no five-card draw event. Want to play it in a casino? No problem if you live in California, own a time machine and can go back to 1978.

Until the recent surge in popularity of Texas Holdem, Seven Card Stud was the most popular poker game played for many years.

Holdem - an abbreviated term for Texas Holdem, which is also spelled Hold'em or Hold 'Em - is a community-card Poker variation that is now the most popular card game in Las Vegas, Atlantic City and other American casinos. Texas Holdem is the game you see in the World Series of Poker on TV.

Omaha Holdem is similar to Texas Holdem in some ways, but the players receive additional hole cards, and the hand must consist of 2 and exactly 2 cards from the players' hole cards and 3 and exactly 3 cards from the board. (As opposed to Texas Holdem, where the hands can consist of any combination of board and hole cards.)

Some poker sounding games are really not poker: Caribbean Stud, Let It Ride and Pai Gow Poker are casino games played against the house with some poker elements.
They is not really a poker game, in that players do not bet against each other.

Caribbean Stud Rules
Five cards total are dealt, which are all facedown. The dealer receives five cards also, but with one of them revealed. At this point, all players examine their hands and act. They can either fold and lose their ante bet (as well as jackpot bets) to the House, or, they can stay in the game by making a call bet, which is double the amount of the ante bet. Remember, the only strategic choice you have as a player is during this phase of the game. Your initial five cards are the only ones you will receive, so be sure they have a chance at beating the dealer's hand.

After all players opting to stay in the game have put up their call bets, the dealer/casino will reveal its four facedown cards. If the dealer's hand does not have at least an Ace/King, the casino automatically loses. Even if the dealer's hand contains a better high card than a player hand with absolutely nothing, the player will still win since the dealer's hand did not qualify with at least an Ace/King. If the dealer does not qualify, players are paid even money on their ante bets only, and are given back their call bets. If the dealer's hand does indeed qualify, it is compared to each players hand according to standard poker hand rankings. If it ranks higher, the player loses both the ante and call bet to the House. If the player's hand wins, the casino pays even money on the ante bet in addition to bonus earnings on the call bet. Since Caribbean Stud is a progressive game with a payout structure somewhat similar to a video poker machine, the amount of the bonus earnings on the call bet depends on the casino call bet bonus schedule.
See: http://www.onlinecasinoconditions.com/poker/caribbean-stud-rules.html

Five Card Stud probabilities

Five Card Stud
Hand	Combinations	Probability
Royal flush	4	0.00015 %   1/649,740
Straight flush	36	0.0014   1/72,193
Four of a kind	624	0.024   1/4,165
Full house	3,744	0.14   1/694
Flush	5,108	0.20
Straight	10,200	0.39
Three of a kind	54,912	2.1
Two pair	123,552	4.8
Pair	1,098,240	42.3
Nothing	1,302,540	50.1
Total	2,598,960

Calculations at: Poker1.com, Ivars Peterson's Mathland, mathforum.org

Five Card Draw probabilities
I couldn't find general probabilities of ending up with certain hands after the draw.

Initial hand you receive	Example	Cards you want to draw	Odds for drawing the cards
4 card straight- missing card on two sides	J T 9 8	Q or 7	5/1
4 card straight - 1 card missing in one place	J T 8 7	9	11/1
4 card flush	K 9 7 4, all hearts	Heart	4/1
4 card straight flush - 1 card missing in one place	7 6 5 3, all hearts	heart or 4	3/1
4 card straight flush - 1 card missing on two sides	7 6 5 4, all hearts	heart, 8 or 3	2/1
Two pair	8 8 5 5	8 or 5 (full house)	11/1
3 card straight flush - 2 cards missing in both sides	9 8 7, all hearts	Straight or better	11/1
Three-of-a-kind	J J J	J J J J or J J J - -	9/1
Three-of-a-kind and a kicker	J J J Q	J J J Q Q or J J J J	9/1
A K same suit	A K, all hearts	A A K K or better	13/1
Pair	Q Q	Two pair or better	3/1

Source: Poker4Real.com

• Probability for improving a pair to trips (three of a kind) or better is 12.76%
• If your hand has two pairs, you can improve it to a full house with odds of 10 to 1. This means every 10 games you'll get 1 full house.
• If you draw three of a kind, and want to improve it by drawing two cards, your odds are 9 to 1 against you.
• If you have a partial double ended straight missing one card on either side, and you draw one card, your odds are 5 to 1 against you for reaching the straight. If the straight has a gap in the middle or has a single end, the chances drop to 10 to 1 in the five card draw game.