I am not in a completely fasted state when I workout, but I definitely make sure I don't have food in my stomach when training. This means no food up to a few hours (as many as 6) before a workout.
There are multiple reasons for this... first, there are some days where I push myself and having food too soon from a hard workout might waste the food (throwing up).
Second, I cannot find the article, but there was a myriad of benefits to workout out fasted reported by Art DeVany. Unfortunately, those articles are only referenced in the googlesphere at present, and I'm having the damnest time trying to find the original.
Third, After years of believing the preworkout/postworkout nutrition jive, I'm happy to report that it just isn't that important for me to workout with "optimal nutrition" before and after the actual training. I've had the best workouts of my life and set some of my best PR's on an empty tank.