Now this is one neat tool for anyone wanting to monitor certain terms on Twitter. Tweetbeep markets itself as Google alerts for Twitter, and it sure seems to be!
You may want to keep an eye open for mentions of your Twitter name (although Tweetdeck and similar software also provide this functionality) or look for potential new clients searching for information on a product or service you provide. You may want to follow certain people and be emailed when they have asked a question. You can look for tweets that are deemed to have come from certain places or locations, or include a certain hashtag, or reference a certain person. There are plenty of options for customising your alerts to include specific search terms and keywords, and Tweetbeep can also endeavour to discover mentions of your URL even when hidden behind a URL shortening service.
There is a limit on the free account of 10 alerts, but upgrades are available for a mere $3-20/month so the premium accounts are worth investigating if you want to make the most of this software.