These are some of the games I recommend to people:
Fluxx - a card game where the rules change every hand.
Small World (by Days of Wonder)
Shadows Over Camelot (also Days of Wonder)
Settlers of Cataan - start with the basic game, though you may want the expansion set (for players 5-6).
Roborally - great game, if you can find it. I think it is finally back in print.
Dread Pirate
Formula De is supposed to be pretty good, although it is pricey
I have one of the Carcassone (Hunters and Gatherers, I think), and while I have not gotten to play it, it looks fun.
LMK if you need more. I have some friends who are real board game buffs - I merely dabble.