Getting Rid of Vegetable Pests Organically?

I have a vegetable garden and it seems that each year it is being plagued with some sort of problem. The first year was great, the second year, I had a problem with aphids. The third year, it was vegetable fleas? The next year, it was mildew and this year I am already seeing vegetable fleas. Is that the correct name for the little black shiny bugs that hop like fleas? If so, how do I get rid of them for good, using organic products?

By Emma H