It is really easy to do this. If you are using Windows computer, you can transfer photos from iPhone to computer directly.
Step 1. Plug your iPhone to your computer
Step 2. After your computer recognize your iPhone, open your "computer". There will be a folder for your iPhone. All the photos on your iPhone are here for you. You can copy and paste the photos as you want.
If you are using Mac computer, you can use iPhoto to do this. It is really easy to do that.
There also some third party software can do this job for you, such as iPhone Transfer software. This software can not only transfer photos from iPhone to computer, but also transfer photos from computer to iPhone directly without iTunes. It can also transfer music, videos, movies, messages, contacts, playlist and other files between iPhone and computer. It can also transfer files between two iPhones.