The Fallout Series. Master of Orion 2. The Civilization series. Master of Magic.
These are, imho, the absolute best.
Fallout was mature, back when it was released this was something very rare and if a game was directed at adults, it consisted mostly of either blood and guts or boobs. Or both. While not good for children, I wouldn't call it mature
Fallout though, oh boy. Choices, morality, no black and white situations. And of course the setting is cool.
Master of Orion 2 - much better than the disappointment that was it's sequel, it's my favorite 4Xgame (eXplore,eXpand, eXploit, eXterminate). Designing your own ships, creating an empire, it's never been as fun as it was here.
Master of Magic - an old strategy game that looked and played like a cross between civ and an rpg game. Build cities, develop them, crush your enemies etc .. but also hire heroes, arm them, level them up, research spells, fight monsters, travel to another planes of existence... there was a lot to do.
Civ series - Hell, I'm addicted to these time stealing bitches. Steam is showing me almost 400 hours of civ5 ....I could write pages and pages about it. i won't. You're welcome.
As for shooters, a honorable mention must go to Unreal Tournament, the game of my High school, my first real online experience.
Yac.