Okay.
I read the title and I thought "Yay, strategic board games!" I'm a big board/card game fan:
strategic: gipf project games, other games by Kris Burm; go, caylus... (for some reason or other I can't get the hang on chess)
I like other board/card games (more-than-two players ones where you need some luck) too: settlers of catan, whist, bridge, ticket to ride, genius,...
And of course pen-and-paper role playing. Our style of role playing has nothing to do with strategy any more, but it is fun.
The posts in this tread seem to indicate computer games. I like civilization IV (with some mods making it bigger and longer) The only drawback seems, if you're playing hotseat, one of the human players gets often ahead well before the Middle Ages... and the other resigns. I've only played one game till the end. It was a super close tie between me winning cultural victory and husband winning the space race! (He won. He has sent a spy blocking the production of my best city for a few turns and that made the difference.)
I don't think board games are superior to computer strategic games. They are older (duh). They have simpler rules (which I like). I don't think there is an objective rule saying which game is better than the other. There is only subjective preference.
All strategic games I like are turn-based. They are either very abstract (not featuring a theme, such as the battle theme of chess) or empire-building. I like the abstract ones because of their complexity combined with really simple rules. I like the empire-building ones because I like building and creating.