Lots of things can go wrong, but …
Make sure you’ve downloaded the right version of Blender for your OS
If you’re on windows, make sure you have the right to install programs.
If it still doesn’t work, please give more details on your OS and Blender version.
VERSIONS:
My Operating System is Microsoft Windows XP Professional Version 2002 Service Pack 3.
When downloading, I have always been selecting from Windows 32 bits.
USER RIGHTS:
I will try to check on this and let you know by tomorrow please.