I'm confused at why some people here are going out of their way to make Da Vinci's achievements sound trivial in the most fuzzy ways without providing any actual clear facts.
'he did not contribute anything new...'
The truth is much of his work was lost and/or only discovered later, so by the definition of 'contributing' to the direct development of particular fields, it wasn't nearly as impacting as it could have been. I don't see how that reflects on his 'genius' in any shape or form. Instead it demonstrates ignorance and it's a point that someone who actually is just a little read up on Da Vinci wouldn't make.
We only have a fragment of his work documented today, and just on that alone, his brilliance in the many fields he was interested is clearly observable.
'he was an excellent illustrator'...
That's like looking at his anatomical drawings and concluding he's a great illustrator without really understanding what he was drawing.
Only fairly recently has it been discovered exactly how well Da Vinci understood the workings of the aortic valve and blood flow. He used similar methods of flow visualisation that researchers used to make similar findings about the working of the heart in the 1990s (source http://link.springer.com/article/10.1007%2Fs00348-002-0478-8...). It took over 500 years for the field to catch up in that respects.
He figured out why the sky appears blue (requiring understanding in optics and physics), the cause of heart disease, created some of the first robotics. If Da Vinci's work was accepted and published out in the open during his time, his impact on several fields would be highly influential.
'Hardly any of his engineering worked'
For a better appreciation of his engineering prowess, maybe check out some of the many attempts to replicate his machines. Granted some sketches (which is what we're left with) don't work as is (if that's what you're expertly judging), but as is the case with engineering, you learn by iterating designs and testing real models, a luxury not given to Da Vinci for each of his many projects.
(And I wonder why people keep replicating his work if he was such an ordinary engineer)
A lot of those experiments to replicate have been made into documentaries and are good fun to watch. Here's an interesting attempt to reproduce his diving suit design http://www.youtube.com/watch?v=YjzZ1-Plgjs.