Most large cruise ships, and even some of the smaller ones (Crystal's 1,000-passenger ships, for example), will have an onboard casino.
The major exception to the big ship rule is Disney Cruise Line, which does not have a casino on any of its four cruise ships.
Norwegian Cruise Line's Pride of America also does not have a casino.
Most expedition ships and river boats do not have casinos.
All cruise ship casinos have numerous slot machine options, and most have table games as well, including blackjack and a variety of poker games (Ultimate Texas Hold'em, Caribbean Stud, Three Card, Let It Ride) that you play against the dealer.
For Texas Hold'em played against other players, some ships will have dealer-dealt tables (Norwegian Cruise Line, most Royal Caribbean ships), while others will use electronic Poker Pro tables (Carnival Cruise Line, Princess Cruises).
Still other ships will not offer Texas Hold'em at all; Silversea doesn't offer poker of any variety.
There's usually also at least one roulette table and one craps table, and a rare few will have Baccarat. But they offer so many variations of ways to win that, at 1 cent per variation, your 1 cent bet can easily end up costing you more than $2 a go.
Very few cruise ships offer truly high stakes gambling.
On some ships, like select Royal Caribbean ships, if enough high rollers want to play a high stakes game, the pit boss may arrange a game. Most cruise ships with a casino will offer tournaments of some kind. Most tournaments are buy-ins where you pay a certain amount to enter and then don't actually spend money during the tournament.
Some cruise lines allow you to rebuy during blackjack and poker tournaments, so winners tend to be whichever player is willing to continually rebuy.
Winners of tournaments typically win money but on some ships, namely Royal Caribbean, winners of the Texas Hold'em tournament receive a free cruise for two on which the final Royal Poker Tournament is held, for which a prize pool of $100,000 is guaranteed. Cruise ship casinos are only open when the ship is out to sea or in port in a select few countries where gambling is permitted (at least on the cruise ship), such as Bermuda and Malta.