I have used my Sizzix machine. They have a die cut that fits a 4x6 picture. I glue it to posterboard I haven't tried thicker cardboard. I then press down and it makes about 8 or 10 puzzle pieces. I then write 1's or 2's or 3's on the back of each piece so it my twins get ahold of all of them I can get them back together.
I used to do something similar with my students. I would copy a picture (from coloring book or anywhere) onto cardstock. Then they would color it and cut it into pieces. With younger kiddos, I would draw the lines to cut before I made the copies. Store it in a zip loc and it's a neat and fun craft that is great for small motor skills.