I was looking around for a way to get a user's public Instagram feed as an RSS feed without using the Instagram API when I came across this question on Stack Overflow.
Probably the best way to do this, would be to use the Instagram API. However, I had no desire to sign up for an Instagram account.
Initially, this answer on Stack Overflow suited my needs quite well. However, as fate would have it, Instagram changed its HTML output and the page's JSON data structure changed. Since the idea is quite simple (we're just screen scrapping here) I decided to write my own script. If this works well for you, consider upvoting my answer on Stack Overflow: http://stackoverflow.com/a/25559442/1171790
EDIT August 2017: I no longer support this scipt. The Instagram HTML output of any given user page changes often and it's been a fun game of cat and mouse but I no longer have a need for an I