I was asked this one today. The answer depends on a number of factors including age, history of injuries, distance, intensity, fitness level, cross training, and how interested you are in "streak running". I could be wrong, but I believe Ron Hill has the longest recorded running streak in history, one that began in December, 1964, some 46 years ago.
So my answer is "You don't have to." Some runners are very tuned in to weekly miles and seem to respond very well to higher totals that require running 7 days a week. My opinion is most runners would be better off supplementing their running with biking or another activity one or two days every week rather than forcing themselves out the door for a sluggish 30 minute recovery jog.
There are exceptions. Throughout the year, every runner goes through different phases in their training. During a build-up when I am not concerned about speed, I like to get out every day and run approximately the same length of time or distance just to build a solid endurance. There may be days that my legs feel dead, but over a 2-3 week period I'll run every day. Once I start adding in long runs however, especially at my age I have to take off the next day to allow a better recovery. I'll still bike or swim though.
Here is a decent article by Amby Burfoot from 2004 that describes a 3 day a week marathon training program. If you try it, I do recommend cycling or some other aerobic activity on most of those other 4 days.