In their debut in 'Mega Man V' (Rockman World 5 in Japan), Mega Man and Roll are attacked by Terra while on a formerly quiet walk. Terra (Earth, in the original Japanese) informs Mega Man that he and his soldiers, the Stardroids, will conquer the Earth; Mega tries to fight him off, but is quickly beaten.
When Mega Man reawakens, Dr. Light tells him that the Stardroids have taken over much of the Earth. He also says that while Mega's Buster was useless against Terra, he designed a new weapon to replace it, the Mega Arm. Armed thus (haha), the blue bomber went out to win back the world.
In the usual sequence of clearing stages and fighting bosses, Mega Man defeated the nine Stardroids, including Terra. (He also re-encounters Enker, Quint, Punk, and Ballade, and fights Dr. Wily once more, but this site isn't about them!) When Wily is defeated, he releases Sunstar (a.k.a. Sungod) to destroy Mega Man, but the robot shoots him first, before turning to the hero.
After a tough battle, Sunstar falls. (Unless the player is not too good at the game, anyway. ;)) Mega Man offers to take him back to Dr. Light's lab to be repaired. Sunstar, at first confused by his willingness to forgive, refuses and tells him to leave, saying that his reactor is going critical and will destroy the entire fortress. Mega Man leaves then, and the space base explodes.
And that's all of the Stardroids' involvement in the game series.