Are there big waves of entrepreneurship over time? In some models there are times when there are many entrepreneurs, and others when there are not. Is this a stylized fact of some kind? Are there any statistics about how entrepreneurial a particular generation is?
I think there are waves indeed. When you look at historical evidence you see a swinging between 'more free market' and 'more central planning (thus less free market)'. The more free a market is (less regulation, less taxes), the more entrepreneurship you will see. 
In the Soviet-Union for example entrepreneurship was dead because everything was centrally planned by government. It made no sense taking risk or sticking your neck out for something.

For statistics, if I were you I would try to look for historical data about 'number of people self employed', 'number of starting businesses', ... Maybe you can start by looking over here: http://www.oecd.org/std/business-stats/ or here http://ec.europa.eu/eurostat/web/structural-business-statistics/entrepreneurship/indicators

hope this helps a little