Google Instance ID
Released at I/O 2015; on Android requires play services 7.5.
https://developers.google.com/instance-id/
https://developers.google.com/instance-id/guides/android-implementation
InstanceID iid = InstanceID.getInstance( context ); // Google docs are wrong - this requires context
String id = iid.getId(); // blocking call
It seems that Google intends for this ID to be used to identify installations across Android, Chrome, and iOS.
It identifies an installation rather then a device, but then again, ANDROID_ID (which is the accepted answer) now no longer identifies devices either. With the ARC runtime a new ANDROID_ID is generated for every installation (details heredetails here), just like this new instance ID. Also, I think that identifying installations (not devices) is what most of us are actually looking for.
The advantages of instance ID
It appears to me that Google intends for it to be used for this purpose (identifying your installations), it is cross-platform, and can be used for a number of other purposes (see the links above).
If you use GCM, then you will eventually need to use this instance ID because you need it in order to get the GCM token (which replaces the old GCM registration ID).
The disadvantages/issues
In the current implementation (GPS 7.5) the instance ID is retrieved from a server when your app requests it. This means that the call above is a blocking call - in my unscientific testing it takes 1-3 seconds if the device is online, and 0.5 - 1.0 seconds if off-line (presumably this is how long it waits before giving up and generating a random ID). This was tested in North America on Nexus 5 with Android 5.1.1 and GPS 7.5.
If you use the ID for the purposes they intend - eg. app authentication, app identification, GCM - I think this 1-3 seconds could be a nuisance (depending on your app, of course).