Wow, some interesting and inspiring answers so far!
Some of the games you mentioned I already own: Settlers of Catan, Axis and Allies, Puerto Rico, Hero Quest.
Also I have played Thunderstone at a friends, which should be something like a clone of Dominion. But from what I've read, Dominion might be better - through the expansion sets alone. Thunderstone, well, hasn't really fascinated me very much.
Yes, card games count, too!

I love playing the Lord of the Rings LCG, Warhammer: Invasion (I just bought the Cataclysm expansion set, I am eager to test it!!) or the Game of Thrones card game (but I don't like the deckbuilding mechanism of GoT LCG too much, because to play it in an interesting way, you need a lot of expansion sets and every player should have the basic game, because of the free choice of plot cards and the choice of neutrals).
I can contribute Mage Knight to the discussion, which is really a good board game for players, who liked the old DOS game Warlords on PC.
Currently a friend has borrowed me the Game of Thrones board game - I am very curious about it and will most likely try it the coming weekend!
I have to google the other games you mentioned!!