The original Instagram website and API client
This was the first web app that displayed profiles of Instagram users online. It was done by using Instagrams private API. Despite the fact that Instagram now displays user profiles on their official site, this app is still online.
The process of sniffing out their private API is described in my post: Creating the missing Instagram web interface.
Nowadays Instagram has an official API and many 3rd-party web sites that do interesting things with people's photos and data.