Hello Kawa123,
I've had that problem before. Something is corrupted somewhere in the phone, usually related to the download manager or the cache.
What I suggest is if you're knowledgeable with Android, go in your settings, then applications, manage applications. In running apps, look for Android Market, Market and download manager. Stop those three. After you're done, go in all applications and look for Android Market, market or Vending, click on it, do clear data, clear cache. If you see a button called "uninstall updates", do that. Now go back to the all applications list and look for "Download Manager" and clear cache, clear data again... Do uninstall updates if you see that button too.
Once you're done, reboot phone and try again... If it STILL doesn't work, do a factory reset on the phone... Back up all your files, documents, etc. and then do this:
VOLUME UP + HOME + POWER
It will ask you if you want the phone to be reset to factory settings. If you backed everything up, say yes and then try again with the downloads...
Good luck!