Why can't I download games, apps, etc from any site except the Official Android Market?
You can allow your device to install non-Market apps by going to "Settings" > "Applications" and checking "Unknown Sources". This should allow you to install non-Market apps although your settings menu may be slightly different. 

Once you have it enabled check out this question if you need more info.

If you are on AT&amp;T in the U.S. you should check out this question.