We just upgraded the Technology in the Arts blog to WordPress 2.5 and I'm jazzed. The new version has so many new features back here on the administrative side of things: an auto-save feature, a simpler interface, and access to great plug-ins (or widgets). The process was quick, painless, and transparent to our loyal readers. But, we didn't just trust to luck that it would be so. When performing major system upgrades, here are some rules of thumb I like to follow:

Learn as much as you can beforehand. Does the product have a blog or a press release that will walk you through what's new? Are there any forums or discussions with additional insight about upgrading? Investigating before you upgrade will give you a jump start on the inevitable re-learning you'll need to do and it will also help you to decide whether or not the upgrade is worth doing in the first place.
Backup everything. Is there a chance something could go wrong? Absolutely. So backup everything (or as much as is practical). Before upgrading our blog, we backed up our files and database, just in case.
Put your foot in the water. If you have the ability or the luxury, perform the upgrade in a safe, test environment before applying it to any live or working systems.
Have an escape route. Even if you've tested the upgrade and it worked perfectly, always expect the worst. Have contingency/restore plans in place and the necessary tools and staff at hand should something, Spock forbid, go wrong.
Don't forget about the learning curve. Any upgrade is going to require at least some sort of re-learning on the part of the user. If the upgrade is significant, or if you have many people who are affected by the upgrade, don't forget to spend time developing a training plan before you move forward.