Steam has a feature which I quite like and that is the ability to upload and download save games.
Unlimited saves would be questionable but three per game sounds like a fair amount.
Is this planned for GOG, would anyone else like to see this? Anyone think that prohibitive issues would be involved?

Highly unlikely. Would add a lot more bandwidth costs to GoG, and would probably piss off a lot of the community who think Steam is the work of Satan.
That being said, this thread is what you want.
http://www.gog.com/en/forum/general/howto_online_storage_and_sync_of_save_game_files

@Gundato
Interesting, thanks for that link.
Yea I don't like steam much, if it was the only choice then maybe I would use it but having GOG as an option (no DRM, no pricing regions!!!) means I shun Steam. However that doesn't mean I won't look at them and want features they have.