What is the best IDE to develop Android apps in?
LATEST NEWS
Android Studio has officially come out of beta and been released. It is now the official IDE for Android Development - Eclipse won't be supported anymore. It is definitely the IDE of choice for Android Development. Link to download page: http://developer.android.com/sdk/index.html
NEWS
As of Google I/O 2013, the Android team has moved to IntelliJ Idea with the new Android Studio IDE: http://developer.android.com/sdk/installing/studio.html
Great to see Google endorse Idea. It is safe to say that Android Studio, and thus Idea, will from now on be the definitive IDE for Android development! :D
ORIGINAL ANSWER
IntelliJ now has support for Android. See Enabling Android Support from the JetBrains help page and the Google Code project page for the plugin. The Getting Started wiki page is pretty helpful.
If you are used to IntelliJ, I don't think it would be beneficial to switch IDEs just for Android tools. You can work on Android with any text editor (I use Vim). If you're more productive with a specific environment I don't see why you'd have to learn a new one. Not worth it in my opinion. Plus I'm a big IntelliJ fan. The IntelliJ plugin lets you make apk files and push the app to the emulator, that's all you need for Android app development. I'd say you're safe sticking with IntelliJ.
Update: there is now an official free IDE for IntelliJ android dev! http://blogs.jetbrains.com/idea/2010/10/intellij-idea-10-free-ide-for-android-development/
Eclipse is not that hard to learn (I use both Eclipse and NetBeans, and I switch back and forth pretty effortlessly). If you're going to be learning Android development from the start, I can recommend Hello, Android, which I just finished. It shows you exactly how to use all the features of Eclipse that are useful for developing Android apps. There's also a brief section on getting set up to develop from the command line and from other IDEs.
Of the existing IDEs, Ted Neward ranks them this way:
Best: IntelliJ IDEA
Second: Netbeans
Third: Eclipse
He seems to think that Eclipse throws up a lot of "friction"; hard to say what that means.
Edit, years later: After attempting to use Eclipse/Aptana for node development and using JetBrains products for node and ruby development I would absolutely start with IntelliJ IDEA and give that a try for the 30 day trial.