Lots of companies have built great applications using Flex. Here are some of our favourites. Others have compiled lists of great Flex and AIR applications as well.

Mixbook - Create beautiful photo books online.
Activa Live Chat - Leading enterprise level live chat service that is fully available online - in the cloud.
Picnik - Photo editing the easy way, in your browser.
Sliderocket - Amazing online presentations.
NVidia - CUDA Zone for developers.
Sherwin Williams Colour Visualizer - Discover how coordinating paint colors and bringing your color ideas to life is easier than you ever imagined.

Adobe has used Flex extensively for online applications, including:
Acrobat.com - Online word processor, spreadsheet and presentation tool.
Photoshop.com - Online photo editor.