I highly recommend Terra Mystica.
It has a lot of rules, so your first play through will take a few hours, but once you get the hang of it it's surprisingly straightforward (yet deeply strategic).
Very well balanced and very little luck.
If you're after something quick and not too heavy, 7 Wonders is awesome.
Best thing about it is that it plays really well with any number of players from 3-7.
Turns are simultaneous, so it's a quick game no matter the number of players.
Through the Ages is a good one if you're looking for an online league.
Check out the
Boardgaming Online website and click the link to the forum at the bottom if you want to play in the league.
Only caveat is that it's not exactly a newbie-friendly game; games take a long time and early mistakes will hurt you badly later on.
Battlestar Galactica is just plain awesome.
I don't know, I could go on forever.