Every business should have either a Board of Advisors or a Board of Directors. Period. There is no wiggle room in that statement, except for one thing: If you are running a lifestyle business, or if you're not really serious about succeeding in your business, then... save yourself some trouble and forget about it.
However, if you really want to succeed, and not waste your time, and want to take the shortest path, with the least stress, then get yourself a Board.
What's the difference? A Board of Directors is a legal entity. The Board of Directors is there for the purpose of representing the interests of the shareholders. They hire and fire the CEO, they approve the business plan. If you are the CEO, you want a happy Board of Directors, or else you will not be CEO very long.
A Board of Advisors is for a CEO who owns most, or all of the stock. Such a CEO is not going to be fired by his Board of Advisors, because they have no legal standing, and the CEO can do whatever he wants. His Board of Advisors is there simply for the guidance.
The benefit of having a Board comes from having regularly scheduled meetings, usually once a month in young companies, but as little as once a quarter in mature, profitable, and stable companies. You want your Board to be actively involved in the challenges and plans of your company. That's why you want to meet, formally and regularly.
If you are doing a startup, and going to need some angel and/or VC capital, you have some special considerations. Check out this article for more on that.
And, finally, here's a very good article in INC magazine about some details on setting up boards of advisors/directors.