I should know better, especially because the Apple Genius told me to do this, but I was so preoccupied with other features...
If you have upgraded from an older iPhone, and done a Restore using iTunes, FaceTime will NOT be activated even though it is active by default on a new iPhone. The act of restoring turns it off.
To remedy this, go to Settings -> Phone and toggle the switch for FaceTime.
Now I'm ready for my closeup!
enable facetime
Here's a step by step guide on how to do it:
http://blog.caneja.com/tips-tricks/iphone-tips-tricks/enable-facetime-on-the-iphone-4g/