My new smoke detectors have a battery back up, even though they are hard wired. Do I have to turn off the power to them to replace the battery?
No. Are you afraid of a shock? They're low voltage.
The batteries are low voltage - the smoke detector is 110.
When you take the smoke detector off the mounting, you will need to unplug the wires that go into the detector. For most designs, the wires have to be unplugged before you can access the battery. The plugs are designed to not expose any AC power.
I never turn off the power to mine when replacing the batteries.
Say what? I've never seen a smoke detector like kayakboy describes. Most these days have an separate battery compartment that doesn't involve removing the smoke detector. Even those that don't you don't have to disconnect anything to remove it from the base plate to change the battery, you can just leave it dangling by the supply wires. The 110V area covered up so there's no problem doing so live.
ronnatalie is correct. When I said they were low voltage, I was thinking of the ones I have that are wired into my security panel, but there are plenty that run off of 110V. However, there are no exposed wires in the box they are mounted on. Even if you have to remove a 110V detector to replace a defective one, there is typically a two-part plastic harness that wire-nutted to the power; the harness snaps apart and you can usually get a replacement unit that snaps into the old harness. I have had battery-only detectors that required dismounting, but all the hard-wired ones I've had experience with always have had a little battery access door on the outside.