Since I'm not actually using Twitter right now this won't affect me much, but anyone who is should turn on HTTPS by default if you use Twitter via the web:
To turn on HTTPS, go to your settings and check the box next to “Always use HTTPS,” which is at the bottom of the page. This will improve the security of your account and better protect your information if you’re using Twitter over an unsecured Internet connection, like a public WiFi network, where someone may be able to eavesdrop on your site activity. In the future, we hope to make HTTPS the default setting.
Via Twitter Blog: Making Twitter more secure: HTTPS