How can I remotely send an SMS message through my Mac from my iPhone? Is there an application for Mac OS X which would allow me to remotely send SMS messages through my iPhone? Ideally, just a simple application or maybe a full screen remote application like TeamViewer.

I prefer a free solution.
You can use myPhoneDesktop.

This solution has an iPhone and Mac (or Windows) client and sends a push notification from the Mac app to the iPhone with the information for a call, text, URL, text or an image. The iPhone app then opens the data sent to it by the Mac app.

The iPhone app costs $4.99 in the App Store and the Mac app is free. myPhoneDesktop requires an account to be set up, but it is free.