Android 2.2 has a cool service for sending messages to phones: Android Cloud to Device Messaging. "The service provides a simple, lightweight mechanism that servers can use to tell mobile applications to contact the server directly, to fetch updated application or user data."
A simple way to use this service is to send a link from your browser to an Android device. Chrome to Phone is a Chrome extension that makes this possible, assuming that you also install an Android application on your phone. The extension has been recently updated and you can use it to send links, phone numbers and text from web pages.
There's also an unofficial Firefox extension called "Send to phone", which offers similar features. The Firefox extensions adds an option to the contextual menu, so you don't have to click on the toolbar button to send some text.
Some things you can try:
* send a Google Maps link and the Google Maps app from your phone should handle it
* send a link to a YouTube video and the video should start playing on your phone
* copy a phone number from a web page and send it to your phone
* copy a short text from a web page (<1KB) and send it to your phone's clipboard.
Note that you need a device that uses Android 2.2 (Froyo), which is officially available for Nexus One, HTC Evo and HTC Desire. Motorola Droid will be updated to Froyo starting from next week, while other phones will be updated in the coming months.