I always loved the idea of having two heads, but a single consciousness. It is hard to imagine but it is fun to try. You could actually multitask instead of just switch between two tasks constantly! It would be very useful.
This wonderful piece I commissioned was done by @marzimaned on twitter.
Link
GaruuSpike
Interesting idea. Considering that the brains of the two heads ARE directly connected via the spinal cord, it's not out of the ballpark to say that the two heads are the same person instead of different people.