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For example, I know Salamence learns Fly by levelling up.

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Salamence, I mean Salamence xD

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Update for Gen 8 :D

Fly: Salamence, Rayquaza, Fletchling, Fletchinder, Talonflame, Vikavolt, Drampa, Flapple

Surf: Tentacool, Tentacruel, Slowpoke (Kantonian and Galarian), Slowbro (Kantonian and Galarian), Slowking (Kantonian and Galarian), Staryu, Starmie, Omanyte, Omastar, Suicune, Mudkip, Marshtomp, Swampert, Milotic, Spheal, Sealeo, Walrein, Tapu Fini, Eiscue

Cut: Farfech'd, Kartana

Strength: Machop, Machoke, Machamp, Pinsir, Mudbray, Mudsdale, Stufful, Bewear, Cufant, Copperajah

Waterfall: Gyarados, Goldeen, Seaking

Rock Smash: Galarian Farfetch'd, Galarian Zapdos, Mudkip, Marshtomp, Swampert, Riolu, Lucario, Sawk, Mudbray, Mudsdale, Passimian, Golisopod, Tapu Bulu, Clobbopus, Grapploct, Sirfetch'd, Falinks, Cufant, Copperajah, Duraludon, Kubfu, Urshifu (Rapid Strike and Single Strike)

Whirlpool: Shellder, Cloyster, Gyarados, Kingdra, Wailmer, Wailord, Frillish, Jellicent, Dhelmise

Rock Climb (USUM): Venipede, Whirlipede, Scolipede, Scraggy, Scrafty, Ferrothorn, Druddigon, Rockruff, Lycanroc (All forms)

Of course, HMs are unneeded in Gen 7/8, but these are technically still HM moves.

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Surf: None
Fly: Salamence, Rayquaza
Waterfall: Goldeen, Seaking
Cut: None
Strength: None

Rock Smash: Sawk
Whirlpool: Shelder, Mudkip, Wailmer, Wailord, Clamperl, Huntail, Gorebyss, Piplup, Prinplup, Empoleon, Buizel, Floatzel, Finneon,Lumineon, Phione, Manaphy
Rock Climb: Venipede, Whirlipede, Scolipede, Scraggy, Scrafty, Ferrothorn, Druddigon

Source: Used the search bar for the site which tells us which Pokemon learn the move and how.

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Gorebyss and Huntail learn Dive at Level 37 in Gen 5 games, where it's an HM. I doubt this list is complete.
That's an answer from 2013
Pokemon Black and White came out in 2010. This answer should have included them.