1.) Although the upgrade may add new features that you don't think you want or need, it may also be fixing a flaw that previous existed in the program, or making the program more secure. It's easy enough to say "my site is secure it's never been hacked" until the day it is... it's a good idea to update for these reasons.
2.) Is your other software compatible with the upgrade? One example is, your hosting company is running PHP 4 and there is nothing you can do to change it. The upgrade of your software now requires PHP 5. In this case you really can't upgrade, and if you try to do the upgrade anyway things might get messed up.
3.) Are you running add-ons or mods? Lots of the bigger and more popular scripts (like Wordpress, phpBB, Joomla, etc) spawn lots of add-ons and modifications that you might have installed on your site. Be sure that when you upgrade these mods will still be compatible, or that you can live without them.