Jigsaw Puzzles from Titan Inc is an excellent free jigsaw puzzle app. It produces digital jigsaw puzzles from any of thousands of images in the library of available images, and these puzzles are easy to deal with since there are no actual pieces. You can set the app to create puzzles of various styles and difficulties, and you can use your own photos to generate jigsaw puzzles if you upload them to the app.

You can create puzzles ranging from 9 pieces all the way up to 1600 pieces if your device has a sharp enough resolution to support such a high number of pieces. If not, the app will automatically generate a puzzle with the highest possible number of legible pieces. The number of puzzles in this app would cost thousands if bought in a store, and you won't have to worry about losing any pieces over time.

You can create your own background music with files you already have, and you can download all the content for puzzles from the app to use at your discretion. The background image of the playing surface can be changed to anything you want it to be, and you can save your creations to the SD card if there is one.