These packages are the most popular and flexible ones for combining images:
• Jahshaka – free, open-source video editor and compositor. This project seems to have risen from the dead.
• Blender is technically a 3D program, but it has powerful effects and compositing abilities as well.
• Natron not only promises the usual compositing tools, it seems to work with plugins for well-established compositors like After Effects. Free and Open Source.
• It’s Windows-only, but Wax offers some of the same capabilities. Your mileage may vary.
• Adobe After Effects offers a 30-day trial at Adobe.com.
• Nuke – The former in-house compositing program at Digital Domain is now a major industry tool. There is a 15-day trial available here.
Online fora are good sources of information about how specific products work and for user-written extras that might be useful.
Lots of video editing packages offer compositing options as well.