Ideally you need to go a week or two without shampooing to allow your hair to adjust. The thinking on this (and I don't know if it's based in science) is that your scalp is producing excess oil because you keep washing it away. When you stop using shampoo your scalp will, over time, slow down its oil production.
I have very dry skin, so I can't comment definitely on whether those theories about oil production are based in truth. I can detail my own experience, though.
I used to shampoo daily and had terrible issues with dandruff. A couple of years ago I decided to stop using shampoo as an experiment. After about 3 weeks my dandruff cleared up completely. These days, the only time my hair gets shampooed is when I get it cut - around once every 6-8 weeks. For a few days afterwards my hair feels very limp and my scalp is very dry and flaky.
I do make sure to rinse thoroughly with warm water on a daily basis.