"The Quake series is a line of first-person shooter video games produced by id Software.
The Quake series is somewhat unusual in that its focus changes frequently: the story of Quake II has nothing to do with Quake, and Quake III Arena has little to do with either of its predecessors. This is mostly because Quake II was originally intended to be a separate franchise ("Quake II" was a tentative title), a plan which was shot down when most of the names id Software had tried to use instead were already taken.
Quake involves a Marine traveling through alternate dimensions to prevent a demonic invasion, a storyline similar to that of id's previous hit game Doom.
Quake II involves an assault on an alien planet, Stroggos, in retaliation for Strogg attacks on Earth. Most of the subsequent entries in the Quake franchise follow this storyline.
Quake III has minimal plot, but centers around the "Arena Eternal", a gladiatorial setting created by an alien race known as the Vadrigar and populated by combatants plucked from various points in time and space. Among these combatants are some characters either drawn from or based on those in Doom ("Doomguy"), Quake (Ranger, Wrack) and Quake II (Bitterman, Tank Jr., Grunt, Stripe).
Quake IV picks up where Quake II left off, finishing the war between the humans and Strogg. The spin-off Enemy Territory: Quake Wars acts as a prequel to Quake II, when the Strogg first invade Earth."
Source: Wikipedia, "Quake_(series)", available under the CC-BY-SA License.