Panels only appear in one workspace

I would reset all gnome settings and configure it from scratch. That is rename the whole .gconf directory.

There are related settings in a few other subdirectories of .gconf, probably guessing what exactly causes that behaviour is something only a gnome expert can do ;)

Renamed .gconf, logged out, logged in, flipped through workspaces. I still only have panels on workspace one. And my desktop icons went bye. Fortunately the only ones I had were shortcuts to places in the file system.

You can always restore your former settings by deleting current .gconf and renaming the old one back.

If this is not enough lets try some more renaming, gnome settings are actually in a couple more places:
.gconfd, .gnome, .gnome2, .nautilus, .metacity

That didn't work either.

*sigh*

Do you maybe use some kind of new window manager, like compiz, or just the standard ubuntu 7.04?

Try the same procedure but login in recovery mode (press esc when "grub loading..." appears), or use a live cd.
To rename a directories from the console do:

cd <path to your home directory>
mv .gconfd .gconfd.old2

That's because some parts of the configuration, state may get saved when you log out. Let me know if you're not experienced with the console etc., i'll provide more details then.

I believe this is where I insert a lolcat reading "Confused Cat is Confused". I don't know what compiz is, and I've spent the past couple days alternately trying to figure out what you're talking about and ignoring the problem entirely. Only, half an hour ago, my computer go boom again. When I got it restarted, it was back on default orange background, which told me something else was screwy in my settings, because I changed my background to blue. So I tried deleting all the .whatever folders named above and renaming the old ones back, thinking further arguing with the computer might not be worth it and it's not like I'm not used to a single workspace from Windows. Except when I restarted the computer after that, the panels were back in all four workspaces. And I should have left it at that, because I restarted again to see if the panels were planning on sticking around this time, and now the panels are just in the one workspace.

GAH.

Sorry for the confusion.

Compiz is a 3d desktop (desktops on a cube, lots of transparency, fading, wobbling etc.), many people install it for better looks, it's also responsible for next ubuntu's versions' (Gutsy Gibbon) desktop effects. There are more desktop managers which you can install instead of the default one -- metacity -- but if you don't know anything about then most likely you didn't.

Honestly, i can't explain why all panels are there after one restart and not after another, maybe gnome, metacity or something else got damaged in that crash. Purging and reinstalling some packages (e. g. gnome-panel) might help.

Given your last comment the chances that resetting gnome configuration will work aren't great. However, a simpler way to try with such a fresh configuration is to create a new user. Either using system-->administration-->users and groups, or typing "sudo adduser mynewuser" in terminal (mynewuser will be the new login, you can use whatever you want here; it will ask you for password). Then, logging in using this new account, try to configure the panels, restart a couple of times, and see if the panels are still there ;)

*blinks at Ubuntu* I was ignoring the problem for a couple weeks, then I upgraded to Ubuntu 7.10, and the problem is no longer there...