A question of sense:
Nearly all twitter apps offer the option to send a message to the twitter user if inside of twitter a new tweet arises. Some of them - like Twidroid (and peep?) - repeat the tweet content and insert it into the android information. Other - like Swift - only indicate the existence of a new tweet. However - repeating the tweet is a little bit silly, isn't it? The twittering user reads the message twice.
Can I twitter by using my T-Mobile G2 touch?
To twitter is necessary - even if bad people say: mostly for the twittering themselves, more rarely for the recipients. Anyhow - the T-Mobile G2 touch is a good medium to become a twittering member of the community:
Firstly the HTC based smartphone brings already along an integrated app named peep: A "green bird icon" marks the tweeting tool. It's indeed a full featured Twitter application that allows you to do everything you can do with the Twitter widget and more. Send and receive direct messages, filter tweets by displaying only the replies directed to you, mark favorites, and even search for new Twitter users to follow.
Secondly the android app store offers also the two most famous twitter applications, Twidroid and Swift:
On the one hand Twidroid is the most famous app and has been reviewed as an excellent Android app. It's also a full featured Twitter application which seems to have at least one additional feature: a search by which one can get a broad stream of tweets which one still doesn't follow. In the net there is at least on statement announcing (proving?), that the HTC application peep could be a 'clone' of twidroid.
On the other hand Swift is a nice alternative which also does, what a Twitter client should does. But note: While being installed the app only requires the access to the network, the geo location and the systemtools. Nevertheless inside of itself the app has activated its option to send all (anonymous?) user data to the developer of Swift. For me this seems to be a little bit strange. Hence I've deactivated the option - without being limited in the use.
Finally I want to mention the only (?) one open source twitter app, named Twitli. At least one internet site has reviewed it as an excellent simple app. But most of the android market comments have referred to slowness. And indeed - even if I love open source - this app practically doesn't work: I couldn't get any messages.