As with many things, I'm a later comer to boardgames. Sure, I've played Monopoly and a few other classics in my youth, and I did follow the Magic craze for a bit, but then I gave up on it all for years.
Just recently, I have discovered a few games that have caught my interest, such as Fortune & Glory, A Touch of Evil (owned) and the Pathfinder Card Game (potential future owner). I also had an encounter with Elder Sign but it didn't work out for me (I guess I like to win most of the time :p)
Being a roleplayer first, I tend to look for games that emulate a story in the least abstract way possible, and I'll (much) prefer solo or co-op games over competitive ones. I do enjoy some challenge, though I'm clearly a step below the average player in that regard.