iTunes maintains a backup for your iPhone, which is updated by iTunes as the first step during the iTunes sync process. This link provides the data included with your iPhone's backup.
http://support.apple.com/kb/HT1766
No additional program is required. You already have it, which is iTunes. When you connect your new iPhone to iTunes on the computer you have been using to sync your old iPhone, you should be prompted to transfer the backup for your old iPhone to your new iPhone. This must be followed by a sync with iTunes to transfer your selected iTunes content - music, podcasts, movies, TV Shows, and 3rd party apps from your iTunes library on your computer to your new iPhone, and for transferring any photos on your computer to your new iPhone.