I dropped my phone in water. Now iTunes says it needs to be restored. How do I get my original pictures off of the phone before restoring the phone and losing all of my information?

There is no way to get them off the device.

Once the iPhone is stating that it must be restored, all data on the device is irrecoverable.

You don't. Heck, you're lucky it even turned back on.

http://www.tansee.com/download.html for PC users

http://www.copytrans.net/copytransphoto.php (PC users)

Also you could try this:

Following are Steps to Transfer Photos from iPhone to MAC:

1). Attach your iPhone to Mac
2). Open up Preview
3). Click File menu and from there select “Import from iPhone…”
4). Select the photos you would like to transfer and click import, Select “Import All” in case you want to have all the photos in computer.
5). For confirmation sake go to ~/Pictures/ folder, picture copied from iPhone should be there.

If you have a windows PC then follow below given procedure to Transfer Photos from iPhone to PC.
You can accomplish this just using Windows Explorer, but there are two different methods. And here you go with the first one.

1). Plug your iPhone into your computer without iTunes running.
2). Now pop-up will appear asking what you would like to do with iPhone.
3). Click on “View Content”
4). Locate your photos.
5). Copy the same and paste it at desired location on your computer.

Another method for Mac users is "Image Capture" which is already installed on your mac, I will look for other applications for mac users, hope this helps!

You can try recboot. Google it. It's a way to get your phone out of recovery mode ( which it is in). also, backup more often🙂