
There is a huge variety of services for Twitter. Here I selected those of them that will be useful for collecting statistics.
1.
TweetStats
TweetStats shows the number of messages by month, the frequency of messages depending on the time of day and day of the week, the highest number of responses to specific people, and the most used clients.
In addition, there are statistics on the words used, which is displayed in the form of a word cloud.
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Twinfluence
TwInfluence is a simple tool for measuring the cumulative impact of tviplov and their followers, and also provides statistics of some social networks as a bonus.
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TweetEffect
Shows how the number of your followers changes after each post.
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Twitteranalyzer
Gives a variety of statistics in several areas: Users, Friends, Mentions, Groups and smaller sub-levels. A lot of information for analysis.
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TwitterCounter
TwitterCounter allows you to track the statistics of the popularity of your account, set up email notifications.
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Twittergrader
Detailed account statistics showing all hits and so on.
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Tweetmetrics
Various statistics of your account.
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Klout
Account statistics, the dynamics of its growth, its twi-force.
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Trendrr
A powerful service for collecting statistics on the Internet, including Twitter.
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Trendistic
The site gives an idea of the popularity of a particular request, and presents its number of repetitions on Twitter on the chart.
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TweetBeep
Allows you to track the mention of your brand, name, website, in general, any word on Twitter, sending you a notification.
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Analytics.ad.ly
Systematizes information about followers.
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TwitterStreamGraphs
An interactive tool that allows you to create a graph based on the words referenced in Twitter users.
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Tweetreach
It will help you find out how popular your tweets are.
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Twitalyzer
The service is designed to analyze various twitter accounts.
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Tweetoclock
It will help to track the time users use their Twitter account.
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Tweetwasters
Shows how much time you spend on Twitter.
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Sledui
Rating karma, polls, frendo meter, etc.
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Radian 6
A powerful tool for analyzing social services, including tools for analyzing Twitter.
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Yahoo Sideline - offline application for searching and analyzing current trends.

-------------------------------------------------- ---------------------------And finally, a bonus, 2 simple but interesting services:
www.sleepingtime.org - the site analyzes the time of your sleep on tweets.
whatsmytwitteraccountworth.com - find out how much your account is worth.