There are a vast number of Twitter applications both downloadable and web-based. There follows a useful cherrypick of the ones that may prove handy for your business.
THE TWO ABSOLUTE MUSTS
Download TWEETDECK from http://www.tweetdeck.com . Completely free and simple to install, you can organise your "tweets" easily pick out tweets that mention you and the tweets you are most interested in. This application becomes essential if you use Twitter regularly and you get thousands of followers.
TWEEPSEARCH http://www.tweepsearch.com is a web-based twitter search engine ideal for deciding who to follow. Use keywords to target clients, suppliers, related industries for networking and target localities.
BEST OF THE REST
All the following are http://www.xxxxxx.com based facilities, so are easy to access:
TWITPIC allows you to share images on twitter
TWITDOC does the same for documents
WEFOLLOW Tracking particular issues being discussed
MRTWEET Analyses your usage of Twitter and can recommend you to others
TWEETLATER helps you automate messages, handy for targeting a particular time.
COTWEET Handy for those who want multiple Twitter accounts, e.g one for business and another for socialising
TWEETBEEP Lets you track the usage of certain keywords.
TWELLO and TWIBS are Twitter business directories
TWEETSTATS offers graphical analysis of your Twitter usage.
TWITALYZER tracks your impact on social media
WHATTHETREND detects hot topics on twitter
and finally TWEEPLER is another way of organising your followers.