WebHarvy can be used to easily scrape tweets from twitter.com. The following demonstration video shows the steps involved.
As shown, using WebHarvy to scrape tweets is very easy. WebHarvy is a point and click visual web scraper, using which data to be extracted can be selected using mouse clicks.
In case you need to scrape tweets after logging in using your Twitter account please make sure that you follow the steps mentioned at http://www.webharvy.com/articles/sites-requiring-login.html.
To know more, please watch demonstration videos at http://www.webharvy.com/demo.html
15 days free evaluation version of WebHarvy may be downloaded from http://www.webharvy.com/download.html