The pry bar is probably the first tool you buy to take pallets apart. If you don’t own it still, that is.
Its main use is to get between the boards and the beams and pry them apart. You can use it also to remove the nails, however, I prefer to use a claw hammer for that, or pincers.
It’s a simple tool that will come in handy in every other odd job.
See my post on Pallet Busting for an instructional video on how well this tool works.