Do pilots pilots keep track of their groundspeed, by head?
That depends on what you have in the cockpit, most planes these days fly with some kind of GPS be it a full blown panel mounted IFR certified unit or just an iPhone app. All of the ones I have encountered either by default or with minimal effort will display your ground speed for you and there is really no need to manually compute it. 

The main purpose of ground speed is to ensure that you actually arrive at your destination with more than vapors in your tank. Let's say you need to travel 100 nautical miles in a Cherokee. You have 1.5 hours of fuel on board which is legal for a VFR flight. You unexpectedly hit a 55 Kt headwind at altitude. You trip is now going to take you a little over 2 hours assuming you cruise out at 100 Kts/Hour. Knowing your ground speed ensures you have the information you need to know that you will need to land ~50 miles into the flight and gas up.

When flying IFR its also important so that you can provide ATC an appropriate time deviation if you are not going to make a way point when expected. 

On a similar note, most decent flying apps will do fuel computations en route for you as long as you provide a performance profile.