Many good thoughts here, for various types of games. One thing I haven't seen mentioned is the scenario for when one player simply knows the rules a whole lot better than the other players -- or when one player knows the rules a lot LESS well than the other players. I've got a player in my game who just doesn't get the rules after playing for more than a year. He's still not always comfortable determining how many things he can do while hasted or when he can make a full attack versus a single attack. So people in the group help him out with that. Sometimes it annoys me, but I'd rather have them help him out than have to say, "Nope, you can't do that," myself every time.
On the other hand, there are times when I as the DM can barely hold back from "helping" the players. The party rogue Just Plain Didn't Search for traps a few sessions ago. They walked into a room. An alarm and trap went off. They all made their saves against the trap. They went, "Huh, bummer on the alarm." The alarm eventually went off.
They went into the next room. An alarm and trap went off -- they defeated the monsters magically summoned by the alarm and saved against the trap. "Man, this is gonna suck."
They went into the NEXT room and said to each other, "Okay, let's all be ready for that alarm to go off, and be ready to help anyone who gets caught by the paralyzation trap." At this point, I was banging my head on the table.
Finally, I said, "Um, guys, you know, there's a small chance that the... DEVICE... that sets off the trap and alarm is something that could be... DISABLED. I'm just saying."
At which point the party rogue said, "No, I don't think it would work," and blithely stepped into the room, setting off the alarm and trap for the third time.
At this point, I decided that the monsters teleporting in from the alarm should spontaneously increase in hit dice.
-Tacky