Tweetminster, simply put, follows the UK political scene through Twitter. It helps you find all the UK politicians that are active on Twitter, but it also organizes these tweets in a wonderfuly useful way. You can check out which political party is the most active on Twitter, you can sort tweeters by constituency, and - if a politician is not active on Twitter - you can contact them directly from the site and try to convince them they should join the fun.
All this makes for a very interesting lens of the UK political scene, but the same principle could be used on almost anything; I can imagine a similar service showing and organizing tweets by football players, US folk musicians, astronauts - anything goes.
The service is inspired by a similar US-based service called Tweet Congress, which has flown under my radar until now, and it's perhaps even better, with a map of United States, fancy graphs and statistics for Twitter using US politicians. Hopefully, we'll see more and more similar services based on Twitter as it permeates the mainstream.