This isn't strictly a web application, but if you are a Java programmer then one project I'd recommend would be integrating the Twitter Search API with FreeMind for the purpose of facilitating real time curation of tweets. Real time curation is apparently the number one request for software that the twitter people get, and FreeMind is the ideal platform for curating tweets. All that's needed is a way to intelligently get tweets into FreeMind so that they can be quickly sorted appropriate buckets, and since FreeMind is written in Java it might be a good fit in terms of skill set and project size.
To give an example of how this would be used, the project described above would reduce the time of making this from about seven hours to about an hour: http://www.squidoo.com/Hacking_Education
No, there's a streaming API [0] that allows for access to a subset of the firehose in JSON via search and filtering. I wrote a short ruby script that is a good demo of how it works [1].
To give an example of how this would be used, the project described above would reduce the time of making this from about seven hours to about an hour: http://www.squidoo.com/Hacking_Education
Also, here are two relevant blog posts:
http://scobleizer.com/2010/03/27/the-seven-needs-of-real-tim...
http://shannonclark.wordpress.com/2010/02/19/curate-for-me-a...