Cross pollination does happen, but usually between things that are closely related (think varieties of tomatoes, or varieties of peppers). The biggest issue is that rarely the new "species" is infertile, which you won't discover until the third year. (First year you plant from bought seed, second from seed you harvest, third nothing grows.) It is very, very hard to prevent if you have a small garden and natural pollinaters. What you CAN do to prevent it is bag the flowers (to prevent natural pollination), pollinate them yourself (use a q-tip), and bag until it sets fruit. Save that fruit for seed.
Otherwise, just try to plant things you REALLY don't want mixing as far apart as possible (for me that is just the sweet and spicy peppers) and let nature have it's way with everything else. You might end up with something even more delish in the long run!
I've never worried much about it since things I really want a certian way (like my tomatoes) I just buy fresh seed each year. Other things (like squash) I don't plant enough variety to worry about it. Good luck!