In addition to the other answer which allows you to do a general backup of your phone which may include your photos, you can also download your photos directly to your computer with software such as Picasa (from Google) or Apple software like Image Capture (in Utilities) or iPhoto (which may also be known as Photos). These methods will also preserve the full resolutions of your photos. Obviously, you will need to have a computer on hand and have your phone plugged into it.
You may also want to check in iPhoto to see if there is a photo stream that already has all of your photos online.
Another option, if you still have cellular data, is to download Google's Photos app (or Google+ if you have an old enough version of that app) and you can choose the option to back up all of your photos, optionally over cellular, but that would use up a lot of data.