Venusaur's Frenzy Plant - all other grass starters finals
Charizard's Blast Burn - all other fire starters finals
Blastoise's Hydro Cannon - all other water starters finals ; skull bash - sharpedo, barbacle, avalugg
Beedrill's Twineedle - escavalier
Pidgeot's feather dance - unfezant, swanna, hawlucha, chatot ; gust - butterfree, venomoth etc.
Raticate's hyper fang/super fang - bibarel, pachirisu etc.
Arbok's glare - dunsparce, seviper, zygarde
Vileplume's petal dance - sunflora, lilligant etc.
Parasect's spore - shroomish, amoongus etc.
Diglett's fissure - groundon, whishcash, etc.
Arcanine's extreme speed - rayquaza, lucario, togekiss, etc.
Machamp's Vital throw - throh, hariyama, etc.
Gengar's night shade - ariados, xatu, etc.
Kingler's Crabhammer - crawdaunt, clawitzer
Marowak's bone rush - lucario and mandibuzz
Kangaskhan's dizzy punch - spinda, lopunny, etc.
Staryu's camouflage - sawsbuck, mothim, etc.
Magikarp's splash - wailord, skiploom, etc.
Moltres's sky attack - noctowl, altaria, etc.
Dragonite's outrage - krookodile, xerneas, etc.
Ariados's spider web - galvantula
Espeon's morning sun - beautifly, cherrim
These are all of kanto's and some of johto's Pokemon. There are an excessive amount of Pokemon who can learn the same moves, regardless if it's used for someone only.
Here are all the Pokemon with signature moves: http://bulbapedia.bulbagarden.net/wiki/Signature_move
Hope I helped! :)