Off the top of my head, these are the necessary HM's.
Gen 1: surf, strength, cut
Gen 2: cut, surf, strength, whirlpool, waterfall.
Gen 3: Rock smash, strength, waterfall, dive, surf
Gen 4: surf, strength, rock smash, cut, rock climb, waterfall
Gen 5: surf, strength, waterfall
Gen 4 has the most at six, while Gens 1 and 5 are tied for three. I haven't played Gen 6, so whatever.