Yes, it's possible. In fact, it's the whole idea. There is also content providers, which allows an app to give another app access to it's data. In fact, intents are how an app launches a new screen when you press a button etc - by sending an intent to the system telling it to launch a new activity.

Some of the UX around intents isn't great, but the core concept and implementation is very clever and doesn't get the attention and respect it deserves. Much like many aspects of Android.