Sometimes you need help getting things done, and Basecamp is particularly adept at that. Basecamp is the most popular project management tool on the web (we even use it here at Android Police), but now there's an official Android app with to-dos, discussions, and more. There is much celebration on the team right now.
Basecamp has a mobile web interface, but this app is (thankfully) more than just a web wrapper. This is a native Android app with an action bar, tabs, and a navigation panel. The Basecamp app can access all your projects and includes up to the minute timelines of activity on each one.
The app itself is free, but you can't just start messing around with it – a paid Basecamp account (or trial) is required. If your employer uses Basecamp, you probably already know. Just log in with your account, and you're on the way to the wonderful world of efficient project management on Android.