Generation 1:
* Bulbasaur: No signature move.
Generation 2:
* Chikorita: No signature move.
Generation 3:
* Treecko: No signature move.
Generation 4:
* Turtwig: No signature move.
Generation 5:
* Snivy: Leaf Tornado: A powerful Grass-type special move that can inflict a flinch.
Generation 6:
* Chespin: Spiky Shield: A defensive Grass-type move that raises the user's Defense stat.
Generation 7:
* Rowlet: Razor Leaf: A high-power Grass-type move that has a high critical hit rate. (While not exclusive to Rowlet, this move is frequently associated with it due to its early-game use.)
Generation 8:
* Grookey: Grass Knot: A Grass-type move that deals more damage based on the opponent's weight.
Generation 9:
* Sprigatito: Flower Trick: A Grass-type move that switches the user out after attacking, but the move's power is boosted if the user's stats are lowered.
Note: Some starters learn signature moves during their evolution line. While they may not be exclusive to their first stage, these moves are often associated with them:
* Venusaur: Solarbeam: A powerful Grass-type special move that requires a turn to charge.
* Bayleef: Solarbeam: A powerful Grass-type special move that requires a turn to charge.
* Sceptile: Leaf Storm: A powerful Grass-type special move that lowers the user's Special Attack.
* Grovyle: Leaf Storm: A powerful Grass-type special move that lowers the user's Special Attack.
* Torterra: Earthquake: A powerful Ground-type move that hits both opponents in double battles.
* Serperior: Leaf Storm: A powerful Grass-type special move that lowers the user's Special Attack.
* Chesnaught: Spiky Shield: A defensive Grass-type move that raises the user's Defense stat.
* Decidueye: Spirit Shackle: A Ghost/Grass-type move that traps the opponent and deals damage.
* Rillaboom: Grass Knot: A Grass-type move that deals more damage based on the opponent's weight.
Keep in mind that while some of these moves are associated with the Grass-type starters, they are not always exclusive to them. Other Pokémon may learn these moves as well.