For Delaware startups, only one director is required, but you can have as many as you want. However, as is true for all tech startups, the simpler you keep your startup the better. I usually advise my clients to only have the initial founders be the directors. This keeps the startup nice and lean.
For California corporations, the rule for the number of directors is a little different. In Section 212 of the California Corporations Code, it states that a California corporation is required to have at least 3 directors UNLESS (a) the startup company has two shareholders, then the minimum number of directors is two, or (b) if the startup company has one shareholder, then the minimum number of directors is one.
This is another obvious reason why we prefer Delaware corporations versus California corporations. We represent a good number of startups that have 2 or more shareholders, but we only want one member for the Board of Directors.