I weigh 155 lbs and I'm 5' 3". I need to weigh about 121-135 being that I have a medium frame. I can't seem to lose weight even cutting back on what I eat. How many calories can I take in and lose weight gradually?

Cutting back on what you eat isn't going to work properly if you want to lose weight. Eat more fruits and vegetables if you're feeling hungry. But even that's not enough to lose weight, you need to add some physical activities. Even just brisk walking for 45mins-1h every day once or twice a day will help and you will see improvements in weeks time. You need to exercise for 30mins every day in order to maintain your weight so anything more than that should be good enough.
I'm 5'5'' and I used to weigh 155lbs as well. But since July, I started eating more fruits and vegetables every day and I ate less meat, carbs, and junk food. And now I weigh 130lbs. I didn't even do any intense workouts, I just brisk walked for 1h-1.5h every day once or twice a day. It's more fun and easier to exercise when youre listening to music - It helps prevent boredom.
As long as you are dedicated and determined to lose the amount of weight you need to, then you will. Good luck :)

Oh, and don't feel you need to weigh 115lbs like what the other person said... you can check to see whats a healthy weight by checking your Body Mass Index (BMI) http://www.nhlbisupport.com/bmi/ and go according to that. So for your height and weight, for a healthy BMI, you should weigh no more than 140lbs-ish. So 135lbs is absolutely fine and is a sensible goal to reach rather than 115.

Its not just an issue of calories. Do you exercise? WHat do you eat? It's not as simpe as calories or carbs or whatever nonsense the latest fad wants you to buy into.

What is idealweight for your age, height, gender etc? When you have a general idea where you shoud be, it will be easier to go for a particular target. A 15 year old 130 lb boy needs things that a 25 yr old 130 lb woman does not and the opposite is true.

Second thing is to look at your lifestyle and see what type of meanginful exercise you can do. It will have to be on a regular basis or like diets, you will not keep the weight off. Can you run at least 4 x a week? How about cycling, tennis or other sports? Aim for 30 min minimun of moderate exercise.

Food is another topic, so if you're serious I recommend you read Micheal Pollan and Marian Neste and others.

Avoid the industry hype of low carb, low calorie, low fat, low low low ow....it gets ridicous after a while. People don't realise there is 2 to 3x the profit in that stuff that isn't even good food, much less healthy. Its important to eat real food, but there is people who talk about that in other posts.

under 2000....it takes continually eating 2000+ calories to gain a pound....and that is w/o exercise...if you exercise you will lose weight faster...

lease then you burn.

Depends on how active you are
your metabolism
your health
your nutrients
your hormones
your thyroid function
and your kidney and liver function

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"I cant seem to lose weight even cutting back on what I eat"...

well...this should not be happening...honestly...if everything else remains the same, if you cut your calories, you will lose weight...unless you were gaining weight before and only cut your calories enough to stop gaining weight....otherwise...you probably think you are cutting back on calories, but you really are not...

you need to RECORD everything you eat and teh calorie count...

you also should record your exercise levels...
then you should record your weight...

observe the trends over a month...
then make necessary changes.....decrease your calories, increase working out, and you will lose weight....

Check out this article on losing weight that i found:
www.ehow.com/how_2003077_not-gain-freshman.html

--This article is great because it really talks about the "hidden" food that you eat- for example, you think you are cutting back on calories, but you just "dont count" that cookie. or "just this one time" i will eat pizza....
NO...for good results on weight loss, there is no cheating, and the only way to guarantee this is to hold yourself accountable by writing everything down...

There is a great website for folks trying to lose weight:

www.sparkpeople.com

It's realistic, it asks if you're going to exercise and gives you a realistic calorie range for that. If not, then it gives you another calorie range. You enter what you eat and how much you exercise into a chart. I like that you can really see what you're eating and what it's worth.

Best of all, it's FREE!

You can not lose weight...well, not without, most likely, gaining it back sometime...cutting your diet is not enough. In order to effectively lose weight and be healthy you will need to change your diet and EXCERCISE. Without excercise your metabolism does not increase and simply changing your diet willcause major fluxuations in your weight...be smart.

Less than 2000 calories a day.
If calories required for daily activities even lesser than 2000 then less than the calories actually expended.

Well you need to excessive as well as change your diet or you wont lose weight.