Catan has an Expansion thetthat allows for two more players to join in on the fun. The rules have been adapted for intermediate building phases in between player turns, which helps prevent long downtimes.
Twilight Imperium (Although a pretty hardcore game) allows for 6 players out of the box (iI believe). It also has a pretty cool action sequence system in play that makes all players make small moves one at a time, instead of one long turn. Downtime between turns is also minimal.
For the more lighthearted games : Koehandel (Don't know the english name), The big Dalmuti, Set and Jungle Speed are all 6+player games, which are also quick and fun!