Twitter have just released update 2.1.0 for their official Android app which comes two main and much needed updates.
The first being push notifications. Now whenever you get a mention or direct mention it will come up in the notification area straight away, provided your device is connected to the internet.
The second being the ability to have multiple accounts. A lot of people end up using alternate Twitter apps just so they can have multiple accounts. This update I'm sure is something a lot of people are looking for.
You can download the app right now from the Android market.