boardgames

I really like 7 Wonders, for 3-7 players and one round is also not too long with about 20 minutes ^^

Deception - Murder in Hongkong - for up to 12 people

Mysterium - identify the suspect by looking at abstract cards given by a ghost (goes up to 7 players I think; use the original Ukrainian rules!)
Shikoku - interesting movement game, goes up to eight players
Eclipse - epic space exploration and battles, nine players with the expansion (I've never played it nine players, it would probably take about a week and need a banqueting table to put it on)

A good question and an interesting thread. At five, our group sometimes tries a substantial game like Viticulture or Power Grid. Knowing the game is critical, however, since many complex games are not at their best with five players. When our group hits six, we've recently been playing Mysterium, which is an excellent, simple investigation game with evocative art and a great deal of replay value. It's surprisingly accessible for new players.

With even larger groups, we sometimes play Mascarade. This Bruno Faidutti social deduction game is similar to his later Citadels, but easier to get started with. Another hit has been Bohnanza, although its wheeling-and-dealing style may not appeal to quieter folks.

When we have players who are easily overwhelmed by lots of rules, we tend to fall back to Sushi Go. This is entertaining enough--though beware of playing it with hate-drafting Magic players.

EDIT: It's "Mascarade", not "Masquerade".