We're much more liberal on what pokemon can learn what, just make sure to ask before you invest in anything.
As far as HMs go, cut is no longer an HM, and pokemon who could theoretically do it anyway, now can.
Surf however, does require the oft-sought after HM, as does fly. A pokemon that can fly normally doesn't know how to incorporate it into an attack, nor knows how to let you fly with it. Likewise Surfing pokemon can't quite understand how to let you ride it safely.
Hms are as follows:
Surf
Fly
Waterfall
Whirlpool
Dive
Strength
Dig (For the purposes of excavation)