I've been using this method now for over 20 years (first seen on a cookery programme), but I was wondering what methods others use.
I've seen a few different methods on youtube etc and some even recommend horizontal slicing which appears a bit risky to me (the cut is directed to towards the hand and wrist holding the onion)

My method
1) Half peeled onion
2) Working from right to left, make thin slices - stopping a few millimetres short of the board by tilting knife
3) Rotate 180 degrees to complete first set of slices (I do this to avoid cutting fingers)
4) Rotate 90 degrees - make thin slices all the way through to the board. Finely chop remaining onion slivers from 1)
Here it is in action (he's a lot better at chopping than me though and doesn't rotate as in 3) - has he still got all his finger tips?)
http://www.expertvillage.com/video/76172_chicken-biryani-cut-onion.htm