How do I determine the thickness of wood needed for a desk?
If I were making a desk 3/4" is the minimum that I would go on thickness.  You could definitely go thinner with strapping under but I just like the look.  

If you are worried about flex I would use the sag calculator.  It is great and I use it when I build custom shelves.  A desk should inherently have more support than a shelf but a desk will also have more load - so I believe the the calculations should be pretty close.