You should be able to copy all of your purchases (apps, music, films etc) from your current iPhone to your computer's iTunes via File > Transfer Purchases. As long as they remain available in the store then apps can be re-downloaded, music can be re-downloaded in some countries, and TV shows and films in fewer (and even where films can be re-downloaded not all film studios have agreed to it) - ringtones and audiobooks can't be re-downloaded.
Re-downloading : http://support.apple.com/kb/HT2519
In terms of the apps content and settings, then if you backup the phone to your computer's iTunes then you should be able to restore that backup onto your new phone : how to backup and restore. Passwords (email, router, website) won't be restored onto a different device so you will need to re-enter them on your new phone.
You can also copy photos off your current phone. Just in case the backup and restore doesn't work (it should but it's best to be safe), you may also want to copy any important documents off your current phone as well e.g. via the file sharing section at the bottom of the device's apps tab when connected to iTunes, via wifi, email, dropbox etc.