There are four styles of
betting commonly found in modern
poker games. They are:
No-Limit : you may bet any amount, given that it is at least as much as the largest ante and at least as much as any other bet made during the current round of betting.
Pot limit : you may bet any amount greater than the ante and largest bet for the current betting round, up to the amount currently in the pot. Apparently there is a variation of this, "Half-pot limit" caps the maximum raise at (no big suprises here) half the pot amount.
Spread limit : Bet any amount greater than previous bets in the current betting round up to the limit.
Fixed limit : there is a fixed amount which you may bet at any given betting opportunity. This is the most common bet structure found in American venues. In most of these games (Hold 'Em accounting for most of the tables in any venue I've seen) there are four rounds of betting, with the first two played with a given bet amount and the second two doubling the first. I've seen cardroom Hold 'Em played from $1-2 to $1000-$2000, though $4-$8 to $300-$600 is a more normal range.
The most common poker games found in American casinos and card rooms are limit Texas Hold-Em and limit 7 Card Stud. Other poker variations found are usually limit games. In Europe, pot-limit games are more common. No-limit games are usually only found in high-stakes cardrooms (like the Bellagio in Las Vegas) and in the end rounds of tournaments or specifically no-limit tournaments (like the headline event at the World Series of Poker).
Most (if not all) poker games in casinos or cardrooms are table stakes which means you may not add money to your stake or withdraw money from your stake except between rounds and following a house-defined protocol. If betting exceeds your stake, you may put the rest of your stake in the pot (this is known as going all in) and any bets by other players in excess of your bets is placed in a side pot. At the end of the hand, the side pot winner is determined first from the remaining players, then the side pot winner and the all in player face off to determine the winner of the main pot.
Thanks to koreykruse for some corrections and additions.