If you have not already guessed, I'm a huge Arkham Horror fan. Being a RPGer for over 30 years, I tend to prefer board games that give me that rpg feel to them.
That's not to say I don't like the Euros or some good ol' fashion Ameritrash. Given the choice though, it will be Arkham Horror, Tailisman, Runebound, Fury of Dracula, Battlestar Galactica, etc...
You get the picture.