Quake: Demons from the realm of Lovecraft invade a military base during teleportation experiments. You are the sole survivor of your squad. Go kick some ass. Basically Doom except a lot more brown and 3D.
Quake II: Humans have been at war with the cybernetic Strogg alien race for a while. During a mission where the plan was to send soldiers in with individual pods, your pod is damaged and you are separated from your squad and everyone else is killed. Go kick some ass.
Quake III: Every badass in different dimensions is taken from their world and thrown into the Arena Eternal, where you fight to the death except you don't die. forget storyline.
Quake 4: Sequel to Quake II. Bitterman, the protagonist of Quake II, has defeated the Makron, the Strogg leader. Matthew Kane, you, are sent with Rhino Squad to dispatch the remaining forces. Except they make a new Makron. Then you get turned into a Strogg without the mindloving, so you become a super soldier.
Quake Live: It's just Quake III.
Well they've completely ruined the series then. Imagine if they named Quake 2 Wolfenstein 2 instead and then after that Wolfenstein is nothing but killing cyborg aliens.
You're already killing cyborg Riddler in Wolfenstein, so that wouldn't seem much different from Wolfenstein. And nobody has bitched about the name since forever.