Hi Thifasmom,
For the more stubborn pallets (the ones you cannot break apart cleanly) I always punch the nails through the board rather than trying to pull the nails out (ring nails only like to travel in one direction). I use a good centre punch of about 7mm diameter (with a flat end), a small lump hammer and being right handed a leather gardening glove on my left hand ;)
I've stripped loads of stubborn pallets and in my opinion this is consistently the cleanest way of preserving the boards.
Regards,
'H'