AFAIK, push notifications require a Google account to work (they piggyback on GTalk), so does that mean for apps for the Kindle Fire are doomed if they use the standard C2DM
In addition to Urban Airship (mentioned by stevebot), there are similar alternatives:
Parse.com - I've successfully pushed a notification to the Kindle Fire following their quick start guide. Very straight-forward. It's a tiered freemium model, i.e., free depending the volume. Pricing seems very reasonable, comparatively to Urban Airship and Xtify.
Xtify - Should also work, but I have yet to try it. It uses an XMPP connection to send messages. Also appears to be freemium, depending on the number of devices (currently says under 10K devices is free as a "developer special").
Alternatively, ralight gives some good information and resources for implementing your own push using MQTT in a related thread: Android device needs to be connected to server - C2DM, polling or something third?