To disable autosave in TextEdit.app, run the following command in Terminal:
defaults write com.apple.TextEdit ApplePersistence -bool no
This disables autosave and versions, reenables the "Save As" option and hot-key (Command-Shift S), and reenables Command-D as a hot key for "Don't Save".
For TextEdit, you'll run into sandbox-related permissions errors with this with the old style Autosave, where it attempts to place a file name "filename (Autosaved).txt" in your working directory. I don't know a good fix for that (if someone does, would you mind making a comment?)
This works for other apps as well, just replace TextEdit with the name of the app, e.g.:
defaults write com.apple.iWork.Keynote ApplePersistence -bool no
defaults write com.apple.Preview ApplePersistence -bool no
It is such a relief to have that "Save As..." option back! Hopefully I'll be able to get something done in Lion now with a minimum of cursing.
[kirkmc adds: We know that Save As is coming back in Mountain Lion, but if you want to turn of autosave for a specific application, this is good to know.
I'm not sure about these sandboxing errors. After working with a TextEdit file for a bit, I got an error saying, "You don't have permission to write to the folder that the file "test" is in." To be honest, that kind of outweighs the usefulness of turning off autosave; so if someone can find a solution for that, I'd say this hint might be more useful.]

