Here are a list of tools to perform some analysis on twitter users and posts
I think that twitter analysis data is being sampled by that huge number of twitter accounts who follow everybody.
a fairly good amount of stats and info, about a selected twitter user. Would be more interesting if it would be possible to go back in history for an extended period.
http://www.twitterverse.com/ (not operational on nov 22 2009)
this tracks the most common words seen on tweets
maps relations of a specified twitter account, and tries to identify influences between people (probably analyzing retweets, and list of people followed if taken by another user)
can not evaluate, because it requires twitter username and password, and I do not want to give.
with top followers, top following and top update rankings
interesting web application, which superimposes most frequently twitted words
on top of the world map. zoomable.
A web site for exploration of links. Covers twitter too, and allows to explore relations between people and websites.
this site should be able to identify the tweets that made you gain or lose followers. Unfortunately, it is still in beta as dec 8 2009, and its reports are simply not working.
this application allows to search (use this form of the url) the connections between twitter users.
Of course, complete analyses could also be performed querying the main twitter.com database (this can mostly be done by the company who runs twitter).
reports the most used words appeared in the tweet of a "representative" (and unknown) subset of users
commercial tools for web graphic visualizations. See http://asterisq.com/products/constellation/roamer/demo
check the mentionmap tool, creates a picture of contacts network
twittersheep examines profile and tweeps of a user, then builds a single page, variable-word-size profile. Can be used to quickly get a rough flash of a user personality, as apperaring from his/her activity
provides instant feedback about what is the current "trendiness" of a specific word, listening to what is told in many social communication channels
these sites provide information about a user, collecting as many informations as possible, from many different sources
I will post here more tools as soon as I find them
Marco ( @mgua on twitter )