eBay Desktop is, well, eBay on your desktop. You can use eBay Desktop instead of the website to search, browse, bid, watch items, read and write messages -- most everything that you use the eBay website for to buy stuff. eBay Desktop also goes beyond the web experience through features like desktop alerts (for when items are ending or when you get outbid) and favorite search feeds, which let you spot when items are listed that match one of your searches.
We've made a number of improvements since the private beta (besides changing the name, of course). The number one piece of feedback from users was "make it more about me." We took this to heart and have completely revamped the home screen to put more information about your eBay activity up front. We've made significant performance and memory-usage improvements, and more will be coming soon. The alerts feature now works even when the application window is closed -- eBay Desktop will optionally keep running in the background so that you can get notified when you are outbid.
Remember when it used to be possible to browse on eBay? Well we wanted to leverage the power of the desktop to make browsing on eBay workable again. On the home screen you can drill-down into the categories, all without refreshing.
My favorite new feature is search feeds. eBay has offered favorite searches for a long time, but unless you enjoy getting emails containing your favorite searches, they have been of limited use. Now in eBay Desktop you can access your existing favorite searches or create new ones, and view those lists of items as "feeds" just like you would in an RSS reader. In this view you can see if an item is new, and you can delete items that you aren't interested in.
Download eBay Desktop, and let me know what you think. Feel free to contact me directly (see link in the sidebar) and the application has a built in feature request and bug report widget.