The moments when I feel my mind and my body integrate are when I'm swing dancing and I just get it.
Most of the time when I'm dancing, my thought process goes "one two three-and-four, back straight, five six se-ven eight, keep arms tense, sink weight downward, oh and remember to smile, shit, now I've lost track of my footwork..."
There are rare moments, though, when everything just goes right for a few seconds. Usually this happens when I'm dancing with a more experienced lead and they do a move that I haven't actually learned yet. My mind stops trying to force my body do what it's been taught to do and just lets it respond to the signals I'm being given. For one brief moment everything is motion, mind and body simply move, together, without worrying about where they're going or how they're getting there.
When the motion stops, I grin and think "that was cool!" Then I realize that I have no idea where my feet are supposed to be right now...