Never, ever do an upgrade without backing up important data! Who knows what might go wrong. In fact, never run a computer with keeping regular backups.
This is trivial with a Mac. Buy an external hard drive (they are very cheap nowadays) and use Time Machine. This makes it trivial to restore any or all files. And with Mountain Lion it is almost essential to use Time Machine. Time Machine automatically backs up everything (unless you specifically exclude files or directories) and you don't need to worry about what files you should be copying.