Location: Route 4

Method:
These two Black Belts argue over which Mega attack is stronger. Both are very powerful Normal-type moves, and you can learn both regardless of who you talk to first. The one on the left teaches Mega Punch while the one on the right teaches Mega Kick.

Location: Pewter City

Method:
When you cut down the tree at the northmost end of Pewter City by the museum, you can go in through the back door of the institute to find, amongst other things, a professor who will teach your Pokemon Seismic Toss. This is a great move that always inflicts damage equal to the level of the user.

Location: Rock Tunnel

Method:
Situated near the end of the Rock Tunnel, this trainer will teach one of your Pokémon Rock Slide, a strong Rock-type move with a chance of flinch.

Location: Celadon City

Method:
A bored salesman in the TV department will teach the Fighting-type move Counter, which has an interesting application - it deals double of what the last move that hit it did, if it was in the physical attack type bracket.

Location: Celadon City

Method:
If you return to Celadon City after getting HM03, you can have this old man teach one of your Pokémon the move Softboiled, normally exclusive to Chansey's evolution family.

Location: Saffron City

Method:
The Copycat of Saffron City teaches this unique move after giving her a Pokédoll. It will copy an opponent's move for the duration of your Pokémon's stay in combat.

Location: Silph Co

Method:
This paralyzing Electric-type move will be taught to a Pokémon after the girl hiding in the top left room on the 2nd Floor. It can be taught even after Team Rocket is chased out of the building.

Location: Fuchsia City

Method:
Substitute can be taught just once to a Pokémon if you talk to the boy in front of Kangaskhan's pen in the Fuchsia City zoo.

Location: Viridian City

Method:
This ghastly Psychic-type move is taught by the fellow across the pond in Viridian City - you can either access him through Cut or Surf.

Location: Cinnabar Island

Method:
A very unique move called Metronome is taught by one of the scientists in Cinnabar's research facility.

Location: Victory Road

Method:
Powerful enough for your upcomig Pokémon League challenge, the Normal-type move Double-Edge is learnt from the Cooltrainer near the last ladder of Victory Road.

Location: Mt. Ember

Method:
Sevii Islands' first move tutor (a Hiker) will teach Explosion, an incredibly strong Normal-type attack that leaves your own Pokemon fainted.

Location: Cape Brink

Method:
Two Island's Cape Brink is home to an elderly woman willing to teach your starter Pokémon their most powerful attack - obviously corresponding to the type your Pokémon is. Only one move can be taught, and unlike the other move tutors this one requires you to have a special bond with your starter...in other words, high happiness.

Please note that unlike future generations, other starter Pokémon such as Typhlosion cannot learn these attacks - they are exclusive to the Kanto trio.

Location: Four Island

Method:
The fat man in one of the houses on the island will teach the Normal-type Body Slam, which has a 30% chance of paralysis.

Location: Seven Island

Method:
Learn from a Cooltrainer the last of the tutor-moves, Swords Dance, which raises your Pokémon's Attack stat two stages.