Other answers have noted Jackson and GSON - the popular add-on JSON libraries for Android, and json.org, the bare-bones JSON package that is included in Android.
But I think it is also worth noting that Android now has its own full featured JSON API.
This was added in Honeycomb: API level 11.
This comprises
- android.util.JsonReader: docs, and source
- android.util.JsonWriter: docs, and source
I will also add one additional consideration that pushes me back towards Jackson and GSON: I have found it useful to use 3rd party libraries rather then android.* packages because then the code I write can be shared between client and server. This is particularly relevant for something like JSON, where you might want to serialize data to JSON on one end for sending to the other end. For use cases like that, if you use Java on both ends it helps to avoid introducing android.* dependencies.
Or I guess one could grab the relevant android.* source code and add it to your server project, but I haven't tried that...