Do you eat back your burned calories?

absolutely or some days I would only have eaten 700 calories and that's no good.

Not all of them. I like to leave margin for error.

sometimes. Especially if I'm hungry.

I eat them all back, always have.

I'm in the 'not all of them' camp. Partly because, as others have said, there are margins for error in calorie calculating and I'd prefer to be on the safe side. Partly because I don't feel hungry enough to eat them and I'm a big believer in listening to your body. I put on weight by eating because I was bored or upset so don't want to fall into any other habits of eating for reasons other than hunger and what my body's needs. If I'm craving protein, I need more protein that day, if I'm craving veggies, I need more vitamins that day, etc. Days where I do a reasonable amount at the gym, 800 cals+ according to MFP, I usually end up eating around the 1600 calorie mark. 1,600 calories isn't by design, it's consistently where my levels of hunger put me on those days so I feel that is what my body needs for that level of activity. That said, I do try to eat a largely balanced and healthy diet (but if I feel like indulging or have an event to go to where I'll eat and drink a bit more, then I'll do so with little guilt).

I probably should also add that I've hypothyroidism which slows the metabolism, reduces serotonin and puts the body into stress which increases cortisol and subsequently makes you insulin resistant (unless absolutely perfectly medicated which for me seems impossible and it's safer to be a little under than over medicated) . As a result, if I were to eat the recommended calories for my age, height and sex, I'd put on weight so for me it makes sense to keep a little below.

But different people are using this site for different reasons. Obviously, for those wanting to build or maintain muscle, eating back calories makes absolute total sense. For those of us using this to lose weight - particularly those of us on a longer journey - then whether or not to eat back all or any calories burned is a different and more personal issue. For some losing weight, eating back calories helps in the transition to healthier eating patterns and 'earning calories' is an incentive to exercise more. For others, losing an extra pound or two that month is the incentive to hit the gym and stricter discipline with food works better for them but obviously you have to make sure you're not under-eating and are feeling healthy, energised and sustained.

I don't. Never have.

I never eat back exercise calories.

I dont usually but I have a bad tendency to Under eat when I am in diet mode and when I couldn't budge the scale it was a must to increase but I rarely eat too many of them back. I just try to make sure I am eating a reasonable amount based on my level of exercise. If I run 11 miles for example, I eat more. If I do mild exercise I don't eat them back. Just what I do

I don't.

I exercise after work so if I eat after gym it'll be 10 pm. And I don't eat that late and our doctors always say its unhealthy to eat 2 hours after or before gym.
I do have a protein shake.

If you are really exercising a lot, you should eat back some of those calories; however, they should be protein calories. Indulge in protein after a hard workout.