I look at the KB ARTICLE number, go to http://support.microsoft.com and see if they offer a standalone installer. SOME patches may only apply if you have some other service or feature running and if not, the install fails.

The other big pile of reasons is spyware. A year ago I ran into patches that didn't install and spyware was found on the machine. After that I exclaimed "is there nothing they (spyware) can do?"