apt-get clean just removes the package cache. There's no way* it could hurt anything.
apt-get autoremove removes packages that were automatically installed but now their dependent package has either been removed or no longer depends on them. If you remove a package that depends on things (eg ubuntu-desktop) and then do an autoremove, you're going to end up removing a lot of packages.
This is often done by removing something that a big metapackage depends on. If you look at apt-cache depends ubuntu-desktop you'll see a number of Depends: ... packages. If any of these are removed, Apt has to also remove the ubuntu-desktop package. That's dependency resolution in action. If you then run an autoremove, it'll clean up all those other depends (assuming nothing else depends on them).
Occasionally you might end up in a situation where you want to install something but it conflicts with something ubuntu-desktop depends on. Apt may try to force this through by removing the conflict package (and therefore also ubuntu-desktop). It will warn you about this.
The simple fix is to find out which meta-package you're missing, and reinstall it. This is usually ubuntu-desktop. And in the future READ what apt-get tells you. I don't mean that in a nasty way. I wish I did more often. Upgrading to 14.04 I tanked my whole system back to a very basic command line and had to redownload and install over a gig of packages.
* Life, uh… finds a way™