Some HM slaves I have on various games:
Pachirisu with Flash, Cut, and Dig (also a Pickup slave)
Bibarel with Surf, Strength, Rock Smash, and Rock Climb (my Mt. Coronet slave)
Staravia with Fly and Defog
Kricketune with Cut and Rock Smash
Pelipper with Fly, Surf, and Defog
Gyarados with Surf Waterfall, Strength, and Rock Smash
Kirlia with Teleport (not an HM, but...)
Xatu with Fly
Aipom with Cut, Strength, and Rock Smash
Farfetch'd with Cut and Fly (my "Rotom Form Change" slave)
Then I use some Pokemon who are not slaves for HM use--for example, a Milotic with Surf and a Chatot with Fly, both of whom I'm training for battle.