So the story I've heard is that back in the day Gary Gygax rolled all the dice behind his screen.
Some examples of play in early issues of Dragon and elsewhere did the same - the GM rolled.
In my games, the players roll a lot.
My basic philosophy is that your PC is your playing piece, your representative in the game. You get to roll for it. There is precious little in the game you can control, but you can get to do the rolls that determine your fate. You get to roll to discover the effects and results of your actions.
In my games, this includes but isn't limited to:
- your "to hit" rolls
- your damage rolls
- your defense rolls
- your resistance rolls
- most of your skill rolls (unless they're specifically meant to be rolled secretly in the game)
- your consciousness checks
- death checks
Back in my AD&D days, this was to hit rolls, damage rolls, and saving throws.
I won't always tell you what happens from your roll. You may deal out a triple-damage critical hit and roll 24 cutting damage, and you'll just have to wonder what's keeping the Black Knight still standing after that. But you'll have gotten your rolls.
I won't always tell you what you're rolling for. I might just say "Make a roll - you want to roll low." You get to make the determination, and know whether to cheer ("Yes! I got a 3!") or groan ("Aargh! 18.") "Everyone give me a roll. Roll low."
I'll even give advice on using Luck or not ("I got a 9, do I want to use Luck?" "Yeah, I think you better.")
But I won't take these away unless I absolutely have to. Even then, I'd prefer to let you make the roll even with concealed modifiers and concealed results.
Potential game-enders? I won't ever roll them for you. You always roll your death checks.
It's your guy, your fate should be in your own hands as much as possible.
As the GM, I get to roll for the rest of the game world.
You've got your one guy. Maybe your henchmen or hirelings, too.
But mostly one guy, and the rolls you make to find out how the decisions you made turn out.
And I hate to take that away.