Photography on the iPhone is now known as “iPhoneography” and there are tons of apps for editing, manipulating, and combining photos on the iPhone itself.
Juxtaposer, $3: Combine multiple photos
Image Blender, $3: Photo masking, resizing, combining
Snapseed, free: Lots of adjustments and cropping possibilities
Laminar Pro (was Iris Photo Suite), $5: Lots of photo editing options, including layering and masking
Decim8, $1: Lots of very unusual photo effects
Slow Shutter, $1: Slow down the shutter speed for interesting effects
Glaze, free: Turns photos into paintings
6×6, $1: Crops every photo you take to a 6×6 image
Cropulator, $1: Quickly crop and rotate images