For commercial enterprises,casual twitter users and the curious people like me.These guys provide the data.
Klout - A favourite of mine.
Analyzes and provides data for metrics like followers, who you follow, Retweets,True Reach , Percentile rankings, Trending and how people react to your messages to form a 'profile of your account to form a personality type.
The reason Klout is slower than others is because they do it properly and they also reference and backcheck your twitter data against all their other users so it takes a while.But its correct.
Can be updated every 6 days
Twitalyzer - Speedy service with a Wide scope
Expansive and speedy.Another favourite. Lots of metrics, lots of data.It even allows for comparison between accounts, personality and other useful graphs and charts like Network mapping.
Can be updated every day or so
Tweet Stats - Good amount of stats and a good layout
Get a good amount of data in about 2 minutes. To get your data for your network you would have to wait a few hourse however.A good and fairly holistic site that offers a few features those above do not.
Worthy of mention
TweetEffect -Shows you what tweets made you lose or gain followers and when.
Also twitteranalyzer.com CONTAINS MALWARE. -_-