Hey guys,
MisterMe is being needlessly harsh to the OP. This is what's going on.
Your other account that you sometimes use "owns" the files that you were trying to move from one folder (in the finder) to another folder (the desktop). It doesn't matter that you're only logged in as one user, those files were somehow "created" by the other user, so the OS doesn't really let you mess with them. You could probably copy them or create aliases, but I'm guessing that moving causes issues. The crap thing is that OS X tells you an admin pw is necessary, but doesn't ever prompt you for one. Strange OS behaviour. Anyway, you can change the permissions/owner to those particular files a number of ways. Here are a couple of popular ones:
1) In the command prompt, type chmod XXX <filename> (without the brackets) where XXX is some 3 number combination (e.g. 755, 731, 533, etc...) . This will change the permissions for user, group and owner, respectively. Chmod is a little confusing at first, but it's very powerful and always works. Do some googling for details, and don't EVER chmod 777 just because it makes things work.
2) In the command prompt, type chown <user> <filename> (without the brackets). This changes ownership of the file to whichever user you specify (assuming you have the rights to do so). Also very powerful and it always works. Google chown for more details.
3) Take ownership of folder/subfolder and files using Finder. Like czwolf figured out on his own after being needlessly hassled by you POSIX snobs, you can just highlight what you want to take control of, choose the drop down menu, become the owner, change perms on the enclosed files, and voila! No more weird complaining about an admin password that it never asks for.
Anyway, I thought I'd chime in because this is one of the first significantly bad "error" handling issues I've run into with OS X Snow Leopard, and I was annoyed at the level of snobbery in this particular post. You guys really need to lighten up. Cheers to czwolf and OP for taking the initiative to solve their own problem.