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I use Evernote on every device I use, both mobile and desktop. It is a great tool for doing research online, capturing information, and text editing. I use it daily for all of those functions, and I write thousands of words a day using the editor.
Evernote keeps everything synced with my account in the cloud, always available no matter what device I use. The Android version works well on tablets with an external keyboard for serious writing.
Free on the Android Market
Evernote works well with Skitch, a simple image editor recently purchased by the company. Skitch gets an honorable mention for using with Evernote.
I like electronic day planners, and Pocket Informant is as good as they get. It adds good calendaring to sophisticated task management, all of which can be synced with Google and other cloud services.
The different display modes are fully customizable to build a system that reflects exactly how you like to work.
$12.99 on the Android Market
I spend far too much time on Twitter, and I like the simple display of Tweetcaster. It is easy to read and is full-featured as Twitter clients go. I particularly iike using Tweetcaster in portrait orientation which displays quite a few tweets at a time.
$4.99 on the Android Market (Free version available)