How do people eat 1600+ calories and still lose weight?

Some reasons are:

If they are overweight, it is very easy to eat that number and lose weight still, my goal was 1 pound a week and it set my calorie goal to 1750ish. (I changed my goal to 1.5 pounds a week and now I'm at 1490)

Another thing is many people exercise, then eat back their exercise calories, so while the number you see in calories consumed is 1600-2000, their net calories may be lower than that depending on the amount of exercise they did.

The younger you are, the more calories you need.

They may have an active lifestyle outside of exercise, as in their job and daily activities burn calories for them, so they activity level above sedentary.

You're confusing BMR and TDEE.

Your TDEE (total daily energy expenditure) is the average amount of calories your body burns in a day going about about your normal activities. If you eat your TDEE, you will maintain your weight. Your BMR (basal metabolic rate) is the amount of calories your body requires to maintain optimal functioning of your vital organs and body systems if you were totally inactive or otherwise physically incapacitated. To lose fat while maintaining muscle mass, particularly if you have a small amount of weight to lose, it's generally recommended to eat between your BMR and your TDEE.

Your TDEE is dependent upon a variety of factors, including age, height, gender, current weight, and activity level, so your TDEE may be very different from that of someone else. But as long as you eat fewer calories than your TDEE, you will lose weight. My TDEE is approximately 2100 calories, and my BMR is approximately 1500 calories, so I eat around 1700 calories a day and lose, on average, about a pound a week.

There's a lot of good information here: http://www.myfitnesspal.com/topics/show/912920-in-place-of-a-road-map-3-2013

And here: http://www.myfitnesspal.com/topics/show/1080242-a-guide-to-get-you-started-on-your-path-to-sexypants

I've seen some people say they eat anywhere from 1600-2000 calories a day and still lose 1-2 pounds a week. How do they do that? If their BMR was around 1500 or something, wouldn't they have to burned 100-500 calories every single day just to not gain anything? Am I missing something here?

You don't have to eat less than your BMR to lose weight...your BMR is what your body burns just being alive....if your BMR is 1500 calories, you "burn" that if you just slept all day. I presume one would do more than that. This is what the math looks like...

BMR - Basal Metabolic Rate

NEAT - Non Exercise Activity Thermogensis...all of you day to day stuff form crawling out of bed to dropping a deuce to driving to work, etc

EAT - Exercise Activity Thermogenesis

When you combine these things, you arrive at your TDEE...your Total Daily Energy Expenditure...this is the amount of calories you would need to maintain everything as is....so let's say someone was of average height and weight and worked out some...

BMR - 1500 calories (~ 65% of daily requirements)
NEAT - 450 calories (~ 20% of daily requirments (to include TEF))
EAT - 350 calories (~ 15% of daily requirements)

1500+450+350 = 2,300 calories. Given roughly 500 calories per day deficit would equate to roughly 1 Lb per week weight loss, someone with this BMR and NEAT and EAT could lose 1 Lb per week grossing 1,800 calories per day (2,300 - 500 = 1800)

It is highly dependent on you height, weight, lean body mass, NEAT activity level, and exercise.

I'm a pretty active male and I lose weight pretty steadily right now at 2400 - 2500 calories...but I'm also training hard for a metric century so my weekly EAT can be rather substantial and I may have to up my calorie requirements to slow my rate of loss in the coming weeks.

BMR is completely different to TDEE.
BMR is the amount your body needs at a minimum, to keep your basic functions going, like if you were in a coma. Even sitting around at a desk job all day long, you'd burn more than your BMR. TDEE is how many calories your body needs to maintain it's weight in your usual daily activities inclusive of exercise. Your deficit should come off from your TDEE, not your BMR.

If I ate 1600 calories, even with exercise cals added back, the weight would come off me far too quickly (not that I could stick to that amount anyway) I have no idea what my BMR is, but my TDEE is approximately 2800ish.

I set my daily calorie goal to 1600. My TDEE is apparently 2100 (which seems like a lot). I'm 5'6/150 lbs. Can I lose 1 lb/week this way?

I lose on 2200-2800 a day, as a 5'10 female.
I workout hard and I eat hard too.
I also have a lot of lean mass.

Males and females losing weight......whole different thing; much easier for males

Males and females losing weight......whole different thing; much easier for males

Not always true. I've had no problems losing weight.

I burn about 5000 calories a week exercising....that's how

Same here. Pretty much 5000 calories a week.

My answer to your question is to go to this website: http://iifym.com/tdee-calculator/

My stats:
I am 31 y/o female 5'3" and 162 lbs. On average, I exercise 4 times a week.

TDEE is 2015 - the most cals I can eat in a day before I start gaining weight
BMR is 1420 - the least cals I'm allowed to eat in a day

This means I have to eat below 2015 calories a day, and above 1420 calories a day. I average 1550-1700 a day.

Some days I do eat 2,000 calories, but then the next couple days I'll drop down to 1300-1400 so that for the entire week I have a calorie deficit.

I never, ever eat below 1200 more than one day in a row. I don't have to, and I've been losing 1 lb a week since Jan 1st

Note: These numbers change with every 5-10 lbs you lose, so you have to continually adjust your TDEE when you've lost enough weight.

I'm eating 2400 calories a day and losing about 3 lbs a week. Mostly because I weigh 300 lbs, I work a very demanding job, and in work out like a beast with my personal trainer and on my own 5 days a week. It just depends on each person . My theory is I like to eat, so I'd rather exercise more than cut back more on food lol.

I just need some clarification. My TDEE is about 2100 and my BMR is 1550 so I've set my calories intake to 1700. I understand that I don't then eat any exercise calories back, is this correct?

That is correct for the TDEE method. If you lose weight faster or slower than your goals, adjust calories.

I am 5 9 , 140 pounds and I eat upwards of 2,000 to maintain my weight. I workout 6 days a week, but trust me, chances are you can eat a lot more than you think you can.

They are probably more active. My total calories burned per day is usually 2500-2600. I have a lot of lean mass for my height, an active job, and I work out or do sports about 7-12 hours per week.

My BMR is 1,200 (I am F, 5ft3in, 138lbs) I eat (log my food every day) 1100-1300 cal/day during the week and 1500-1700 on the weekends. Being very conservative, my 4 workouts burn another 2,200 calories/week. I have been doing for 3 months now and I have not lost 1 lb.....pretty frustrating