I'm noticing a trend for creating desktop clients for popular web apps. Twitter is the clearest example; the website was popular, and has a simple and comprehensive API. The whole premise of twitter is based around messaging, so a desktop client is ideal, as it is similar to traditional one-to-one messaging clients such as AIM, MSN Messenger etc. Due to the simplicity of the API, many third-party clients exist.
Other web apps have desktop clients to perform some or all of the web functionality; Picasa, Google's photo sharing website has a great desktop client for editing and managing photos, and uploading them. FogBugz, the bug-tracking web app has a screen-capture tool, and clients for subversion and Visual Studio integration.
For me though, the cleverest desktop client was written by Microsoft, long before the web app existed. I use Google Documents quite regularly for word processing and spreadsheets. Google Documents haven't been around that long, but more than 20 years ago, Microsoft started writing a desktop client for creating word processing documents and spreadsheets, known as Microsoft Word and Excel respectively.
Microsoft waited and waited, and finally a web app was created that did the same thing, and Microsoft in a freak moment of luck, judgement and foresight, correctly predicted the exact format that the Google Documents upload would accept. Documents and spreadsheets created in Word and Excel can be uploaded into Google Documents, and be used in the web app. Amazing. This means that Google (or any other company) need not write their own desktop client - Microsoft did it years ago.