Not entirely sure where to comment here, since there seems to be, like, 3 or 4 different elements of discussion at play: player skill vs character skill, DM fiat vs structured rulings, improvisation vs a strict list of powers...
For myself, in nearly all these categories, I tend to find that it is best to try and find an approach that includes both options, and even has them support each other.
Sure, a player walking up and rolling some dice to find and disable a trap feels less exciting than having them figure out how the trap is worked into the environment and how it can be safely disarmed. At the same time, you don't want the game to turn into 'mother may I?', where the wrong choice - even made by a skilled thief - trivializes their character's capabilities.
As is often pointed out - the fighter's player doesn't need to demonstrate his physical prowess to have his PC behead an orc. Should the rogue's player need to have an actual knowledge of traps in order to have his PC disarm a trap?
Instead, I like keeping both approaches as options, and certainly think that regardless of what is chosen, you want to avoid making it all feel mechanical, so to speak.
Basically, I'm not a fan of rolling a spot check and being told, "Yeah, there is a 20' pit trap in the corridor," or "You find a dart-throwing trap in the wall." Use of descriptive terms is important - "You notice that the ground is structurally weak in the corridor ahead," or "You notice a trip wire along the corridor, and it seems to tie into small holes embedded into the walls."
At the same time, I don't want the characters to be forced to 'figure out my puzzle' in order to know how to bypass the trap, or even realize it is there. Success on the check just telling them... that there are cracks in the ground... goes a bit too far in the other direction.
Water Bob's early example in this thread is the sort of thing I'd fine pretty unenjoyable in actual play. Even when the character succeeds on his skill checks, he has to basically work through the DM's puzzle to figure out what the situation is and how to deal with it.
In those examples, the smart player of the hulking and reckless barbarian will be able to easily find and bypass the various traps, while the less creative player of the skilled rogue will blunder into one trap after another, simply because he can't figure out what tricks the DM is looking for to discover the traps, no matter how well he rolls.
The rolls and the descriptions and the creativity should enhance and support each other, but neither should be the only path to success.
Similarly, when it comes to creative combat actions - like trying to trick two enemies into hitting each other - I definitely agree that letting characters be creative can offer a lot to the game. I tend to prefer having some guidelines - such as pg 42 in 4E - that can help me quickly figure out how to resolve such thing in a balance fashion.
Basically, I like having creative actions that feel like they have a solid result in combat, but I don't want to have to just come up with a decision completely via DM fiat... especially since I feel that risks such actions feeling either not worthwhile at all, or potentially too good. Once a group discovers a creative use of a spell that can instantly turn the tide of a fight... they start to look for ways to use the same trick as often as possible, until it feels more like a loophole than actual creativity.
Now, a really skilled DM doesn't need any guidelines at all, of course. I think that the ability to rule on the fly is a valuable one. But that level of DM skill is relatively rare - and even for a DM that can do so, doing so quickly is even harder.
I would like to see such creativity more encouraged... even in 4E, where you have outright guidelines for such stunts, and the books themselves encourage players to try such things, it is very easy to fall into the mindset that one should just stick with exactly what the character sheet says the PC is capable of. I'm not sure how to find an easy way around that, in the end. And, honestly, a group that has that mindset is likely to be stuck in it regardless of edition, or style of play, or even game itself. Sometimes, that is just how some folks are wired.