Google Cloud Messaging (GCM) is a service that manages small messages to / from android. It does require users to be using google play.
What makes it so cool is they will manage the connections for you. They will queue stuff up for a period of up to four weeks, and after that will send a message telling you that its been more than weeks, and you will need to process a new request to obtain the original messages again.
Its a free service. There are some rate limits, but they seem pretty reasonable. i.e. You can't use it for sending frequent game moves, but its totally fine for normal text messages. As I understand it, GCM is only a server interface. You will have to roll your own XMPP server to store and manage messages. Note: there is a payload limit on GCM messages, I think its 4k or so... not big enough for images. You'd have to manage those via http, and send image names via GCM.
They will also broadcast messages to users (1000 at a time). Did I mention this is a free service?
Something like this link will get you started. The API keys thing and registration #'s is sorta confusing. Once you figure that out, it all works. You can test to your emulator via curl messages to the google server, etc..
Oh, and GCM also keeps track of all your user analytics as well..