This page summarizes information about domino tournaments that can be played online, as well as live events.
GameColony is probably the most popular site for online dominoes tourneys. Players can practice their skills in the Main Hall and then move to the Tournament Hall to compete against other players for cash prizes. There are three game variations: Five-Up (also known as Muggins or All Fives), Draw and Block.
Another option is the Eliters Dominoes League. Eliters is a tournament-based online league where members can test their skills in friendly competition. The competitions are organized at Eliters and played at Yahoo, Pogo or GameDesire.
Live Action Events
Live tournaments are organized periodically in different parts of the world including Las Vegas and South America.
Event organizers include the National Domino Federation (USA) and the city of Andalusia, Alabama. Check their sites for information on upcoming events.