While I agree there are probably some things that are just impossible, I think anything not impossible should be allowed with a skill check.
Sure, it might be hard or even ridiculously hard, but one of the things that I think is cool about 3rd Edition is a fully realized skill system. And I see skills as others have seen them - as another ability, akin to special abilities and even spells, that a character has.
The nice thing about skills is that you don't need to memorize them or get material components, or sometimes even any equipment at all to utilize them.
I made a character with a ridiculously high jump / climb / balance skills, further enhanced by magic, and then that was part of his character - he was one of the 'monkey-like' race in Oriental Adventures. He climbed everywhere, almost never walking along the ground if he could avoid it. With skill levels in about an 8th or 9th level campaign that exceeded 20 or 30 (I can't recall the exact numbers) he could do quite a large number of impressive climbing and jumping. He was a fun and interesting character, and it was because of his skills, in part. It just wouldn't have worked as well if it was about magic spells or other things as opposed to just an inherent part of who he was.
Plus, it is fun to try an do something hard, then roll the dice and see what happens. I have been toying with the idea of a skill roll system similar to what Shadowrun has - if you roll a 20, you can roll again and add the second roll, possibly rolling again if you get a second 20, and so on, though that will require some thought. (And with a 1 resulting in a negative result of some sort).