I love board/card games, even more than I love anime/manga.
Favorites would be:
Power Grid - tense and fun (if a bit math-y), with many expansions for that "similar but different" feeling.
Through the Ages - like Sid Meier's Civilization, except without a map and can be finished in 2-3 hours.
Princes of Florence - Play rival Princes in Renaissance Florence. But instead of competing for money or might, players compete to gain the most Prestige, mainly by sponsoring artists and craftsmen to create great works.