Well, for scifi I'll put a second vote in for Mongoose Traveller. I don't know how well it would hold up as a general system, but I do like the fact that players can trade off initiative and attack bonus to try not to die without quite resorting to a tick system.

Heroic fantasy I'm sold on 5th edition D&D, I can go sorta gritty for crits and 0 hp with existing rules, which is nice. Plus it's damn simple. But if I was going to go with a real blood and guts, swords and sorcery type game I may well be checking out hackmaster from the response in this thread.

Like people say, it's all about what you're looking for. And even the systems I like don't get out without being futzed with.

The Synergy system from Blue Planet v2.0 (FFG) taught my players to respect combat. They learned that combat was deadly, not something to do for fun. They learned that if they weren't taking the enemy by surprise, they were doing it wrong. They learned that if they cleared a room before their enemy could fire a shot, they were doing it right. They learned that recovering from a gunshot wound could take weeks or months.

What did I learn?

I learned that you can run an exciting combat using a rules light/medium system with only three d10's in a matter of minutes. That one damage roll can (and should!) tell me in a matter of seconds if a character is unscathed, wounded, unconscious, or dead. And that rules for grappling, autofire, or any other special case should not be more than a paragraph long.

I really should run that game again sometime....