That whole thing about getting through a game, not with your skills or reflexes, but with your brain makes a victory even more rewarding. Then there are those beatiful different units every game gives you command of; how could I compare driving one character, when I'm in control of a whole army?!
Games like Final Fantasy Tactics, Ogre Battle, and Fire Emblem became inmediate obsessions of my own. But I'm not really into fantasy games as I am about—you know—war games, and Advance Wars remains one of my favorite series of all times; I've mentioned it both as one of my Most Influential Games of All Times, and (just recently) as The Game I'd Play Forever.
Also, I just became obsessed with XCOM: Enemy Unkown when I rented it some time ago, I just don't know why I didn't try it earlier. Now I'm looking forward to get it.
Finally, there's that other title I like talking about, but many people really know:
Operation Darkness, and here's the review I made for GameCola some time ago. And more than just talk about it and giving a score, I even added its very own ESRB rating: