Charades
Charades is a fun game in which competitors take turns acting out something--a movie, book, famous person, etc.--and players from the same team try to guess what is being acted out. Two teams of three work great, and hopefully the six of you will be laughing for hours.
Croquet
If you have access to an outdoor area and are willing to invest in a croquet set, then this could be your game--especially if the weather is nice. Croquet is a game in which players hit balls through a course of wickets. Croquet is a low-stress game that allows for a little competition and a lot of fun times.
Poker
Most card games don't accommodate six players well, but poker is ideal. Whether players are beginners or veterans, a friendly, social game of poker can make for a great time--especially when all that everyone really wants to do is sit around with friends, do a little gambling and swap some stories.
Basketball
Many team sports require a larger number of players. Not basketball. A game of 3-on-3 is a great way for an active group of people to spend an afternoon and work up a sweat.
Apples to Apples
Apples to Apples is a board game suited for groups of six to eight players. Named "Party Game of the Year" in the December 1999 issue of Games Magazine, Apples to Apples is a simple game that is most fun--and revealing--when played with a group of people who don't know one another well.