I just upgraded 3 systems after looking at this page:
https://wiki.ubuntu.com/BreezyUpgradeNotes
The upgrade was from Hoary Hedgehog, which had been kept up-to-date with apt-get. On two of the the systems, I did the full
apt-get install ubuntu-base ubuntu-desktop
before making the changes in the sources.list file to change the version to 'breezy'.
The third system was a server with no GUI, so I just did
apt-get install ubuntu-base
before starting the upgrade, since I didn't want to install Gnome.
One system is an Averatec 3270 laptop; the others are a home-built system with a Jetway motherboard with an 800 mhz VIA cpu, and an older home-built system with a 233 mhz Pentium MMX and 64 mb of RAM - the last one is a server installation.
All the installations went well. When presented with choices for retaining old config files, towards the end of the installations, I chose the default of keeping the old configurations.
On the laptop, a definite advantage presented itself in the case of the OpenOffice word processor and keyboard switching for multiple languages and keyboard layouts. (I have the system set up to switch between US, German, and Russian layouts, with $LANG=en_US.utf8). In the earlier release, it was hard to find a hotkey combination that worked for keyboard switching; in the Breezy release, the Window key worked well for that. In the case of the word processor, there had been a problem with backspacing over and highlighting UTF-8 characters (such as �, �, �, � in German) - the program seemed to be handling the 2 bytes of these characters as separate characters, which was wrong.
I would still suggest downloading the install and live ISOs, as others suggest. But the upgrade went well and fairly fast on my DSL connection.