In This Game, there are multiple Move Tutors teaching us Moves that are not normally seen with this set of TMs so there are people that will teach these moves to you:

These Move Tutors are situated just outside of Mt Moon (Cerulean Exit). The One on the Left Gives Mega Punch whilst the one on the right gives Mega Kick. Here are the Move Details:

Name	PP	Att.	Acc.	Type	Effect
Mega Punch	20	80	85		Deals Damage
Mega Kick	5	120	75		Deals Damage

Situated at the back entrance to the Pewter Museum, this scientist will teach ONE of your Pokémon Seismic Toss:

Name	PP	Att.	Acc.	Type	Effect
Seismic Toss	20	-	100		Causes damage equal to your level regardless of other battle factors

Situated near the end of the Rock Tunnel, this trainer will teach ONE of your Pokémon Rock Slide:

Name	PP	Att.	Acc.	Type	Effect
Rock Slide	15	50	90		May Cause Opponent to Flinch

Situated on the 3rd Floor of Celadon's Pokémart is a person who is willing to teach the move Counter to one of your Pokémon...but this can only happen once so use it wisely:

Name	PP	Att.	Acc.	Type	Effect
Counter	20	-	100		Attacks 2nd, doing x2 physical attack damage that foe did to pokemon

Situated across the Pond in Celadon, this Man will teach your Chansey Softboiled:

Name	PP	Att.	Acc.	Type	Effect
Softboiled	10	-	100		Restores 1/2 of your Max HP

Given to you by the Mimic Girl in Saffron City after giving her a Pokédoll:

Name	PP	Att.	Acc.	Type	Effect
Mimic	10	-	100		Mimics an Opponent's Move for how ever long the Pokémon is out

Obtained by a Woman on the 2nd floor of the Silph Co.:

Name	PP	Att.	Acc.	Type	Effect
Thunder Wave	20	-	100		Causes Paralyze condition

Hiding In Front of the Pen Containing Kangaskhan, this guy will teach one of your Pokémon Substitute:

Name	PP	Att.	Acc.	Type	Effect
Substitute	10	--	--		Takes 1/4 of your HP and creates a Substitute out of it

Situated behind a Bush, this guy in Viridian City Teaches only one of your Pokémon Dream Eater:

Name	PP	Att.	Acc.	Type	Effect
Dream Eater	15	100	100		Only Works When Opponent A Sleep, Gives you half the HP taken by this attack

Located in the Second room of the Cinnibar Laboratory. The Scientist will teach Metronome:

Name	PP	Att.	Acc.	Type	Effect
Metronome	10	-	-		Randomly Does Any Attack

Right at the end of Victory Road is a guy who will teach you Double-Edge:

Name	PP	Att.	Acc.	Type	Effect
Double-Edge	15	120	100		Inflicts pokemon with 1/3 damage inflicted on for

When on the North Part of Mystery Island 1 you will see a Hiker. He will teach you Explosion:

Name	PP	Att.	Acc.	Type	Effect
Explosion	15	250	100		Inflicts a massive amount of damage but causes you to faint

On Island 2, next to the game house, there is a guy that will teach your Pokémon Moves that they had forgotten or that they would have learnt and forgotten before you even caught them (such as Legendary Pokémon). To do this, you need to give the tutor 2 TinyMushrooms or 1 Big Mushroom . These are found attached to Wild Paras and Parasect so it shouldnt be hard to get.