Cut Me In is designed to cut out photos of you or other people and drop them into funny or exotic backgrounds on your iPhone. The app doesn't do it automatically (You'll need to cut them fairly precisely to get a halfway decent looking photo!), but there are quite a few tools here to choose from and numerous background options to sift through as you choose how your final image will look.
After installation, when you load Cut Me In, it will show you a handful of background options. There are many more than this to choose from, however. Just tap any one and you will get a large list of background images and stock photos you can use to drop your cut out photos onto. Afterwards you can choose a photo from your library or take a new one with your camera and cut it out. You'll need a fairly precise finger to cut it out along the lines, made harder by the fact that your finger will be in the way, but with numerous filters and editing tools included to help polish things up, you can make fun photos fairly easily. The interface is intuitive and loaded with options, even if the actual cutting is hard to do, and the backgrounds make it a solid tool for those who want to make goofy photos.
While Cut Me In could use some helpful tools for actually cutting out your photos, it is a solid free app that allows you to create a variety of unique images. The selection of background images and tools for editing what you cut is extensive enough to make this a good app.