I like Topher's response. Sums it up pretty well.
For what its worth, I did my PhD in chemical engineering and now work for one of the major wind energy companies in the world. From a technical perspective, the majority of the engineering staff are electrical and mechanical engineers. Chemical and civil come in behind this.
Another comment I would make is that since a lot of renewable energy business is very new, you get a lot of these engineers coming into the business with little to no experience in it (such as myself) so even though they're coming from different backgrounds, the learning curve is quite similar for each...at least in my particular experience.
If I had to say, since its energy generation, the electrical engineers have the best head start when it comes to understanding things.
Any one of elec eng, mech eng, chem eng, or civil eng would be a good background for getting into renewable energy I think. If your program gives you the option to take courses related to renewable energy in any way, take them.
But this renewable energy is funny when you ask about what background the employees have. You just neve know sometimes. For example, I know some technical people in the materials department and was wondering what engineering dicipline they had studied. Their answer was 'none, we used to build boats'.