The most popular form of Poker today is Texas Hold 'Em where you get 2 cards in your hand, and 5 community cards. Omaha is the same except you get 4 in your hand. Also, unlike in Hold Em, where you're allowed to play 1 (or 0) cards from your hand w/ 4 from the community cards, in PLO you must use 2 from your hand with 3 from the community cards to make your best 5 card hand. Also, the most popular form of Omaha is played Pot Limit, which means you can only bet the size of the pot at any given time.
Of course this makes for a drastically different game. Here are some of the key differences between the games:
* Stronger hands are necessary to win at showdown in PLO. Where in HE 2 pair is a strong hand in most situations, you will often need a flush or better by the river in order to have a strong holding in PLO (depending on the board).
* Hand values run closer together in PLO than in HE. That is, any 4 cards before the flop are usually not a large favorite over any 4.
* 'Drawing' hands are extremely powerful. Drawing hands in HE are almost always an underdog to the 'made' hand, where in PLO the drawing hand can easily have a made hand on the flop in bad shape.
* Pots are bigger in PLO. Because hand values run closer together people tend to play more hands, and since everyone connects with the board more often, there's a lot more action in this game.
* Because hand values change drastically from card-to-card, big bluffs on the turn or the river become near mandatory fairly often, where in Hold Em that's less the case.
2. No Limit Texas Hold 'Em (w antes)
The 'cadillac' of poker, as it was referred to for years, is an excellent game. Unlike in Pot-Limit Omaha, because there are only 2 cards in your hand and only 3 on the flop, there arise many situations where neither player in a hand has either a strong hand OR a strong draw. This has a few implications. First, that you have to bluff a decent amount, at least in small pots, because it's so likely your opponents don't have anything. And secondly, you sometimes have to call bets with fairly weak holdings especially against aggressive opponents. To contrast, in pot limit Omaha you can play a solid, winning strategy by almost never purely 'bluffing' early in the hand (i.e. preflop or on the flop). Though in that game you will sometimes need to bluff the turn or river, as discussed.
In NLHE, again, contrasted with PLO, hand values are much more divergent. In NLHE there arise all kinds of situations preflop or on the flop where you are a dominating favorite over your opponent. Such as your JJ against his 99, or your AK against someone's AQ. Or your AA against their.. anything. Because of this NLHE is a game where your preflop starting hand requirements are extremely important, and having a feel for how people play different types of hands from the very beginning of the hand, preflop, is essential. Whereas in a game like PLO, your starting hand requirements aren't as important, and being able to put people on a 'range of hands' preflop isn't as an important skill. In PLO it's more important to figure out what type of hand they have on later streets than from the beginning. Because the games differ in these ways, there are certain things about NLHE that aren't there in PLO, which are interesting game elements to have.
The 'w/ antes' caveat at the top is there because without antes the game of NLHE isn't as good. It comes theoretically correct to play very tight w/o antes. With antes the game is more loose and more interesting.
3. No Limit Deuce-to-Seven Single draw
We are already entering territory where I have no formal education, outside of general poker theory. But, in this case, i'm not the only one. The highest stakes 2-7 NL games that run on PokerStars are $0.25/$0.5 blinds (extremely low), and the play there is very bad. So, essentially, either virtually no one in the world knows how to play this game, or at least virtually no one likes to, for some reason. In any case, like #1 and #2, this is another 'big-bet' game (as opposed to a 'limit' game), which is my favorite form of poker. And for some reason this game seems to be much more skillful than regular 5-card draw, though that could just be a misconception from my limited experience.
This game has a small blind and big blind, just like NLHE and PLO, and is played like 5-card draw, but rather than making your best hand you're attempting to make your worst hand. It's a lowball game. Straights and flushes count against you, and an Ace counts as a high card. So the best hand in this game is 75432 - no pair, no straight, no flush, 5 lowest cards possible. There's one betting round before the draw, and one after.
I think, for some reason, the fact that the only 'hand values' in the game are lowest card, rather than pair, 2 pair, 3 of a kind, straight, etc. lends itself to a better game for the 5-card draw structure than does 5-card draw, high.
4. 7 Card Stud - High
The top 3 games are really the only forms of poker I like a whole lot, and play somewhat regularly. Limit forms of poker, like 7 card stud, are much less interesting to me. But I still like to play them occasionally.
5. Pot Limit Omaha - 8-or-better
This is just like PLO, but in this game if you have 5 cards 8 or lower then you have a 'low' hand, and you split the pot with the high hand winner. I don't like splitting pots, though, so it's not my favorite game. But it's still pretty good.