The thing that amazed me about Google's gmail was that it acted like a desktop application, but was provided through a browser. Given the limits of client-side and server-side programming, there's only so much you can do and gmail pushed it into a very capable email client I could see using full time.
Flickr just launched a new feature of their photo management/sharing site called Organizr. Watch the demo videos to see it in action -- this is as close to a desktop app I've ever seen a web application. With a bit of Flash programming and photos I've already uploaded, Flickr approaches the features of iPhoto (the photo manager I currently use) and Photoshop Album (tried it, liked it too), but all within a browser. In some aspects (gallery control, keyword additions/searching) Flickr surpasses the functionality of iPhoto.
I can see this is just the tip of the iceberg with Flickr and can't wait until someday I'm storing all my photos there, editing them, posting them, and organizing them all in Flickr.
About the only things blocking this from happening seems to be slow uploading from most home broadband connections (especially with a 5+ megapixel camera) and the unlimited storage problem.