Listed in order of preference/availability:
Nidorina/Nidorino: Cut, Strength, Rock Smash. Evolve to Nidoking/Nidoqueen and you also get Surf, Whirlpool and Rock Climb!
Tropius: Cut, Fly, Strength, Rock Smash, and also the TM Flash which is very useful. This is my favourite HM Slave because it works great in conjunction with almost any water Pokemon. You can get it in the Pokewalker (Big Forest) in HG/SS.
Golduck: Surf, Strength, Whirlpool, Rock Smash, Waterfall, Rock Climb.
Poliwrath: Surf, Strength, Waterfall, Rock Smash, Whirlpool and Rock Climb. If you can't trade, Poliwhirl can learn all those except Rock Climb.
Kabutops: Cut, Surf, Whirlpool, Rock Smash, Waterfall, Rock Climb.
Skarmory: Cut, Fly, Rock Smash.
Rhydon: Cut, Surf, Strength, Rock Smash and Rock Climb. Rhyhorn is rare in Victory Road or Safari Zone but definitely worth getting.
Dragonite is also rare but you get given a Dratini in the game. It can learn everything except Rock Climb, but then you are wasting HMs on a great Pokemon, and it takes ages to level it up.