Android - How do I send SMS from PC through Android Phone or to Android Phone?

PDANet (a tethering program) will let you send and receive SMS via a little desktop client when you are connected to your phone via USB or bluetooth

Update as of May 2015: PDAnet apparently no longer offers its sms agent in its latest version.

If you have Google Voice, you could send SMS that way. If not, you could try out DesktopSMS, an app that runs on the phone and a client app on your computer. That app is available on the Market, and then you can download the PC client from that site.

MightyText is a Google Chrome extension/Android app that will let you compose, send, and receive text messages in Google Chrome by connecting to your phone. So it just forwards received messages from your phone to Chrome, and sent messages from Chrome to your phone.