I've disassembled many pallets by hand with just a wrecking bar or pinch bar. If you take your time, you won't split many boards, but there are generally at least one or two casualties in each pallet.
Remember that any levering method to remove pallet boards is inevitably going to end with a certain amount of broken boards. This is due to the quality of boards used as they are just not premium grade timber and that twist nails are often used.
If you take your time with a pinch bar you will be able to get most boards off. I tap the pinch bar in with a hammer from both sides of the board and lever it often from alternating sides. If you go from just one side the board will often crack.
There are different qualities of pallets out there; sometimes, every board will split no matter what you do. These pallets I move on from.
You can try a tool similar to the Mumme 1260mm Reno Bar which is designed for pallets. I haven't personally used this tool, but it looks effective.
Depending on how many pallets you wish to take apart and whether this will be an ongoing hobby, I'd strongly recommend a reciprocating saw. I currently use a Ryobi One+ 18V Gen II Reciprocating Saw, and it is amazing! With this method, you simply slice through the nails behind the boards and separate them with no splitting at all. With practice, you can disassemble an entire pallet into useable boards in under 5 minutes.
Working with pallets is something I have enjoyed and I would have dis-assembled well over 100 pallets with a pinch bar and hammer. I've got to say it is now a pleasure to be using a reciprocating saw. There are plenty to choose from if you don't need battery-powered or would like something more budget price-wise.
Watch this video. He does choke the hammer a bit. - Brad
I use a fairly large head rubber mallet - increases surface area is more effective and decreases risk of breaking wood. I have a claw hammer on hand to pull out any stubborn nails. Depending on how well it all comes apart and what I'm using the pallet for, I have also run down the sides with a circular saw (a jigsaw would also work). Keep the scraps for kindling. - ProjectPete
I used two flat head screwdrivers and a claw hammer when I first started upcycling pallets. I was able to do a 1200mm x 1200mm pallet in 5 minutes flat with minimal breakages and that is hard work. I now use a Reno bar which I purchased from Bunnings and cost $90, and is a much easier way to work. Work smarter not harder, it will pay itself off in no time. - Kalel2427