What is the name of the genre of games similar to Jetpack Joyride?
They are usually called "endless survival games" and are in the same vein as Canabalt or Robot Unicorn Attack.
Another term for games like these are "infinite runners".
I've heard "auto-runner" on some gaming podcasts, because your character constantly/automatically runs. It doesn't seem to be very widespread though--Googling it mainly turns up task scheduling programs.
According to the developer Jetpack Joyride is in the genre Joyride 'Em Up.
I guess if it's their game they get to decide.