Thud - got it years ago, and have learned the basics but not played very often, and would in no way consider myself much of a strategist.
Ankh-Morpork - bought it on release last year and have played a handful of times. It is very easy to learn, good fun and a great way to use up a few hours. After a few plays you can work on a bit more strategy but it's not necessary to strategise to win.
Guards! Guards! - also bought it on release last year, have played it 2.5 times, with one of those games lasting well over four hours. It is quite a complex game to learn, lots and lots of rules, but hopefully the 2012 reprint (and new rulebook) will make some of them clearer. Once you do get started, it is quite fun to play, but the complexity level is something I wouldn't recommend to anyone who wants a quick casual game - if you enjoy long and complex board games (e.g Risk-style, or many other great geeky ones my friends have occasionally tried to force on me), then it's worth giving it a shot. Just don't panic too much if you forget some of the rules, because everyone always will