While each con has its area of emphasis, just about any kind of game can be found at all four of them and they all include open gaming areas.
The Big Four cons are:
Origins Game Fair
Emphasis: Board games
Notes: Descendent of the Origins Game convention started by Avalon Hill
Emphasis: Historical miniatures
Notes: Originally a regional convention, this has grown into the de facto national convention for historical miniatures gamers.
World Boardgaming Championships
Emphasis: Competitive play of board games
Notes: Originally AvalonCon, this became an independent production after Avalon Hill was bought out by Hasbro. Takes place at the same site as Historicon. There are also "pre-cons" starting the weekend before the main convention begins.
Emphasis: Role-playing and collectible card games
Notes: The oldest national gaming convention.