Seing this thread showed me what the tape should be wrapped up from the outside of the handlebars (left side handle wrapped clockwise seen from behind, and vice versa) but looking at some videos at youtube I see that some does it opposite or say that it doesn't even matter. Is this a matter of the bikers way of holding the handles or is there a strict rule I really should stick to when applying my new tape?
It comes down to your own preferences.
I always wrap mine counter-clockwise on the right side and clockwise on the left side. (seen from riders perspective).. Edit: You probably shouldn't go the same way around on both sides, thoght. The look and feel would be all wrong ;)
The only tricky part is where you go around the shifters.
The idea is to wrap them so the friction against your hands when riding tightens rather than loosens it. I find I have to swap the direction of wrapping as I go past the shifters. Start at the bar ends and go "up the inside and down the outside" (cw on right, ccw on left). If you do an extra loop around the shifters you can change direction for the tops.