Well, I personally think the HM moves are kinda annoying, cuz they can't be deleted without seeking a move deleter.
The HM moves I actually let mah Pokemon keep are the ones that are used to easily navigate around the cites and stuff. And those are Fly and Surf.
Occasionally I'll give a pokemon and let them keep Waterfall, but other than that. I don't really teach mah pokes HM moves.