Active, passive and piezo pickups. Active pickups and piezo-electric pickups will require batteries, while passive will have no need for additional voltage source. In most cases, for regular and low-end guitars, there will be no need for batteries.

Do active pickups work without a battery?

Yes, active pickups need 9V batteries to work. Active pickups have an inbuilt preamp, which requires power to run. If you try to use active pickups without a battery, you won't get any signal at all.

How does piezo pickup work?

The reason is simple: piezo pickups work by picking up the actual vibrations of the string and the instrument. That's why they've typically been used as pickups for acoustic instruments, like nylon-string guitars that wouldn't work with a magnetic pickup.