I am new to gardening and would like to know if I can plant zucchini and
cucumbers in the same raised bed. The bed is about 15 feet long.
I am also planting musk melons. I have several raised beds that are about 2
feet apart.
I have heard that planting these things close will cause cross pollination
and affect the taste of the produce.

This is a myth. Please see this article:
http://www.colostate.edu/Depts/CoopE...t/mythseed.htm
sed5555