I'd absolutely recommend taking a day off every week. I remember reading an article on gold medalist Olympic athletes a while ago, and even they train six days a week and take one day off for rest.
Most doctors and personal trainers would agree that whether you train at an Olympic or casual level, it is necessary to give your body a break. Your muscles repair themselves during periods of rest and recovery, and this means that when you get back to training you'll be even stronger. Without that crucial resting period, you're risking over-training yourself in the long run, which can result in fatigue and even injury. If you get to that point, you'll need to rest and recover for a lot longer than just one day a week.
It's best to avoid that degree of over-training, and therefore I'd recommend taking that one-day-a-week to rest.
