Besides the obvious web, email, and text ways to twitter there are a couple other really convenient ways as well.
Firefox add-on “twitterbar”
This add-on allows you to type your twitter update in the address bar of firefox and then click update within the address bar and it updates your status. You can use this add-on in secure and safe mode to connect to twitter. The add-on also displays how many characters out of 140 you have left to type and then gives you a confirmation message upon saving the twitter status.
Digsby (see my digsby post for more detailed information)
Digsby is a multi-client chat program and social site status update program. The program enables you to talk on all of your favorite instant message networks as well as update your twitter (also facebook and myspace) status directly from the program. Digsby also shows you your twitter updates from the people you are following.
Tweetdeck is by far the best twitter client out there. Tweetdeck is an AIR application so it runs on every platform and is the dashboard of twitter. Tweetdeck allows you to setup several columns of feeds with different information such as specific keywords, groups, and your regular twitter feeed.