I used this procedure to upgrade from 9.04 NBR to 9.10 NBR on an Eee 701 4G. After the upgrade, the internal drive was 89% full. (It barely fits!)

Note: This is a horrible, unsupported thing to do, and you should just do a fresh install. Nonetheless, it's worked fine for me for two Ubuntu upgrades and kept me from having to reconfigure everything to get things just the way I like them. Here we go…

1. Switch to a console via, say, Ctrl+Alt+F1 (do not do the upgrade from within Gnome, KDE, etc.)
2. Make yourself root
3. Run apt-get clean
4. Mount a large external drive, SD card, USB stick, network share, etc., as /mnt/storage
5. Create the directories /mnt/storage/aptcache and /mnt/storage/aptcache/partial
6. Create /etc/apt/apt.conf (if it doesn't exist) and add the following line:
   dir::cache::archives ”/mnt/storage/aptcache”;
7. Edit /etc/apt/sources.list and replace all instances of “jaunty” with “karmic” (or whatever)
8. Run apt-get update
9. Run apt-get dist-upgrade (generally answer “Yes” to things)
10. Run apt-get autoremove
11. Reverse the changes you made to /etc/apt/apt.conf
12. Unmount and remove the external drive
13. Reboot

Enjoy Ubuntu!