1. Might and Magic Duel of Champions
This may or may qualify depending on how you want to define strategy. It is a CCG, but it's the best CCG I have played in a long while. Though it does suffer from some balance issues at the top levels, I've not found too many issues in the low to mid ranks. It's free, though obviously, if you do pay you will get cards more quickly. Ignore most of the rants about how broken the economy is in the game, that's such a high level whine that new players should be fine for long enough until they decide just how much they want to put into the game. I've yet to put any real money in for what that's worth.
This is a java version of blood bowl but it completely annihilates that crap fest that Cyanide put out. Again, it's free, and the community is very helpful and always happy to spread their love of the game to new players. There are a multitude of leagues across all different time zones, several major tournaments per year and simply a lot of variety to enjoy. It is NOT single player though, then again neither is Cyanide. Oh I know, there is a SP mode, but it's such a freaking joke it might as well not exist.
3. X-COM: EW
I still keep coming back to this, and once I start a new campaign I have to finish it. I think this blend of strategy and squad based tactics is my personal favorite kind of game ever. X-COM nails it for me. And, once I get tired of playing around with the various 2nd wave options, i will go back to the Long War mod which makes the game almost completely different while still staying essentially the same. Long War is amazing.
4. Endless Legend
Bought in immediately because I liked Endless Space so much. This is still Alpha so it gets a bit stale as it is missing some features which it needs to round it out, but as others have said, I still find myself drawn to it anyway.
5. Civilization V
I don't really get the gripes about this one. It is damn good with all the expansions. It is still the gold standard in empire builder games as far as I am concerned. I've tried Pandora and various other 'similar' games and they all get uninstalled in short order. I don't really know why, but they are just lacking something.
Games I would like to try at some point (demos plz!)
Warlock 2, though I don't think this one will hold me.
GC3, just to see how it improves on GC2 (which needed quite some improvement for me, not a bad game at all, just wasn't quite my cup of tea)
SotS3, well assuming it happens, and assuming they scrap the crap that was SotS2 and go back to the mechanics of SotS1.
Anything XCOM like! Honestly I know there are other clones out there, but I haven't had the time to really even look for them. I did try Xenonauts, but didn't care for it at all.