It seemed as though something was cutting the blossoms right off the stem and this year I was having the same problem.
So I created a domed cage from chicken wire to put over the zucchini. The next day I noticed that something was still cutting off the blossoms. We figured whatever it is it must be tiny like a mouse to get inside the chicken wire. I decided to do a little internet research. I found this gardening site that explains my problem:
Zucchini plants have male and female flowers. Only female zucchini blossoms can produce zucchini squash. Once male zucchini blossoms have opened to release their pollen, they simply fall off the plant. Many times, a zucchini plant will produce only male blossoms when first in bloom to ensure that pollen will be available when the female blossoms open.
I decided to take a closer look at my zucchini plants and it was obvious that the article was right! The male and female blossoms even look different.

The male blossom is on a long stem and the female is short and close to the vine. The thick, fuzzy part of the female blossom is the start of a zucchini. Here is a zucchini that is further along:

If there is poor pollination from the male blossoms the female blossoms never grow. I guess that is why my garden produced only one zucchini last year. Thankfully, pollination doesn't seem to be a problem this time. Each plant has at least 2-3 visible female blossoms. I can't wait to eat all that zucchini!
I was joking with Michael that nature doesn't vary much in the reproduction process. The male is there to provide the pollination (or seed) and look good and the female does all the work. Then things got out of control with a few vegetable genitalia jokes that I won't sully your mind with. :) Your welcome!