Sent by Emily
Editor - Since you didn't specify whether you were using the iOS or Android version, and more importantly whether you're using a OS X or Windows machine, I'll offer recommendations for both operating systems:
The first is for Mac users: InstaDesk2 is a full featured OS X Instagram client which will allow you to not only view and download your gallery, but also manage multiple users and view those you follow in defined people lists. InstaDesk is going to set you back $4.99, but if you're a dedicated Instagram photographer, it's not an unreasonable amount to pay for such a feature rich app.
InstaBackup for Mac OS X does away with the bells and whistles, honing in on the task of downloading all your Instagram images at one fell swoop. If all you care about is downloading all your images at once, InstaBackup is a low risk proposition at the cost of "free".
Windows users can turn to the Free Instagram Downloader 1.1.1, allowing users to download their whole library...and surprisingly anyone else's by entering their user name!
(Image: Gregory Han)