Please note, that I have included the Gens next to the moves. What this means is that the particular move was/is their signiature move IN THAT GEN ONLY. So that means for example Venusaur line - Frenzy Plant (Gen III), Frenzy Plant was Venusaur's signiature move IN GEN III
Venusaur line - Frenzy Plant (Gen III)
Charizard line - Blast Burn (Gen III)
Blastoise line - Skull Bash (Gen II), Hydro Cannon (Gen III)
Typhlosion line - N/A
Feraligator line - N/A
Meganium line - N/A
Sceptile line - Leaf Blade (Gen III)
Blaziken - Blaze Kick (Gen III)
Swampert line - Muddy Water (Gen III)
Torterra line - N/A
Infernape line - N/A
Empoleon line - N/A
Emboar line - Heat Crash (Gen V, VI)
Serperior - N/A
Samurott - N/A
Greninja - Water Shruiken / Mat Block (Gen VI)
Delphox - Mystical Fire (Gen VI)
Chesnaught - Spiky Shield (Gen VI)
Also note that the moves Frenzy Plant, Blast Burn and Hydro Cannon became available to all the starters in Gen IV only.
Source