First off, Mods, shouldnt this be in System & Software?
Anyway, try repairing permissions:
Macintosh HD > Applications > Utilites > Disk Utility
Then select Macintosh HD in the Disk Utility and press the Repair Permissions button. That should fix the download problem, that is, unless you are trying to download windows programs, which cannot run on Mac and will not be recognized, can you tell me what the extensions of the files you are downloading are?
Example: .jpg, .zip, etc....
It would also help to know what version of Mac you are running. I am guessing at least OS X. Click the blue apple logo in the upper left corner of the screen and select "About this Mac" and tell me what version of OS X it has.
Get back to us on your results.