One of the strongest features of WordPress is that care that has been taken to make upgrading to a new version as easy as possible. I have never had anything but the most minor problems, compared to some CMS software that I tried that failed miserably and I had to abandon.
This time I used subversion to upgrade. I has already setup my installations to enable subversion upgrades, by following clear and simple instructions on the WordPress site. So when it was time to upgrade it was very easy. Firstly I performed a backup (using a backup plugin). I then logged into my server using Putty, navigated to my WordPress directory, ran one command, which ran seamlessly and then did the usual wp-admin/upgrade.php. Everything worked wonderfully.
I hope your upgrade is so smooth!