How important is it to take a "rest"day?

very important.

working out shouldnt cause so much pain you cause permanent damage.

Very important! I hate taking rest days, but there is a piont where I will just be spinning my wheels and getting nowhere if I don't take a break. It gives your body a chance to recover and get even stronger.

Rest is when the muscles grow/repair... adequate sleep, alternating muscle groups worked or leaving a day between each full-body strength routine. It's essential to progress. It's fine to do active rest though; such as light cardio, stretching, foam rolling, yoga, etc

I workout 5 days a week so I have 2 rest days(normally tuesdays and fridays) because your body needs to rest---your muscles need a break--just like you need sleep, your muscles need a break.

As someone else said, you need to give your body chance to repair, especially if you're working out with weights and doing resistance training. You could always go for a walk on your day off?

I work out about 4 times a week, but I have 2 young children, and going out with them and chasing round after them burns up loads of calories, so i guess I don't really have any rest days!

I do Insanity 6 days a week and do P90X X Stretch on the 7th day.

definitely need rest days, i don't like sitting around and doing nothing on rest days either, so i do light exercises at home (moving furniture, yoga, stretching, going for a walk)

recovery is important! especially if you want to build muscle

I rarely take a rest day. The exceptions are the day before and after a marathon, the day before a half marathon (no need for the day after) and if we are traveling I tend to take the day off. I won't be working out next Sunday however I am helping to put on a full distance triathlon and will be there from 4 am until about 2 am the next day...I think that constitutes a work out It is up to each person and how they feel but I don't find it necessary. What I do is mix up my work outs with running, cycling, the Arc at the gym and weight training. My body is well adjusted to working out daily but if I do feel sore I do something that is a bit easier on my body such as the Arc. It is a method that works well for me.

Let's define "rest day" here. A "rest day" is a day where one isn't training the same exact muscles as the day before with resistance. You can do cardio EVERYDAY, but you shouldn't do resistance training on the same muscle on consecutive days. You CAN train say arms today if you did legs yesterday.
So you don't have to rest between workouts, just don't train the same muscle consecutive days. You should try to allow for at least ONE full day of rest and no exercise a week though.

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very important.

working out shouldnt cause so much pain you cause permanent damage.

the pain I have is from my infusions. Not from working out.
Sorry I didn't explain that very well.

Then you aren't able to workout hard enough to put a load on your body so it must improve physically.

You might as well just walk every day. now, if that's what you are doing, great and easy fat burning workout - great.

You are having changes cardiovascularly of course, but even there, not as great as could be had if the body had a chance to recover. And that will stop eventually.

Don't worry though, if you don't give it rest, it'll usually find a means of making you give it a rest. From being sick more often because your immune system is shot, to getting injured for a couple weeks.

And all these negative effects are made worse by eating at deficit, which is another stress on the body, beyond exercise.

So it's really up to you, do you want your time and effort and energy to get the most return for what you put into it (most folks being limited on time), or reach a work plateau where you really aren't getting much benefit from what you put into it?