Are there are good uses of Partial Classes outside the webforms/winforms generated code scenarios? Or is this feature basically to support that?
I often use partial classes to give each nested class its own file. There have been some architectures I've worked on where most of the implementation was only required by one class and so we nested those classes in that one class. It made sense to keep the files easier to maintain by using the partial class ability and splitting each one into its own file.
We've also used them for grouping stock overrides or the hiding of a stock set of properties. Things like that. It's a handy way of mixing in a stock change (just copy the file and change the partial class name to the target class - as long as the target class is made partial too, of course).