"willingness to help others" - I'm very happy with most aspects of my personality

From the MIT application:

What attribute of your personality are you most proud of, and how has it impacted your life so far? This could be your creativity, effective leadership, sense of humor, integrity, or anything else you'd like to tell us about. (*) (200-250 words)

"I'm very happy with most aspects of my personality, but the one that I value the most and which I am sincerely proud of is my willingness to help others. I have the attitude that if I am able to help someone who needs it, I cannot justify not doing so.

This shows itself in many different ways. I was a tutor for math and physics in school, and would often discuss and give feedback on other's work. Even though this has made me sort of a "go-to" person for any kind of help, I'm happy to do it because it helps me as much as the person I'm helping. At a local school for disabled children, many parents of children with communicative disabilities were unable to afford certain speech generating devices for their kids. Looking at the devices, I knew that they had very simple soft- and hardware, and were clearly over-priced. It wouldn't be hard to write software that converts any desktop or tablet PC into a "Talker". I felt compelled to help them, and my father and I developed such a program, which is now being used in the whole school, free of charge.

This attitude is also a large part of why I want to attend MIT. I feel that with the opportunities MIT can provide me with, I will be able to truly have an impact on the world, and to make other people's lives better."

I'm struggling a bit with the 250 word limit, could any of you see something in this that I could omit or rephrase without taking away from the essay?

Of course any other advice and criticism is also welcome!

Yes, take away that first sentence and start with this one, which I love.
Always try doing that. The first sentence of what we write often does not contain the coolness of it. The first sentence is often a warm up. Let the reader figure out the details on her own. Just start with this:

I have the attitude that if I am able to help someone who needs it, I cannot justify not doing so.
You gave an impressive example.

You can also kill that last sentence. It is unnecessary baggage, dead weight weighing the essay down. It seems necessary, but actually the reader can figure it out on her own. :-) Kill the first and last!!

I'm very happy with most aspects of my personality, but the one that I value willingness to help others the most . I have the attitude thatIf I am able to help someone who needs it, I cannot justify not doing so.

This shows itself in many different ways. I was a tutor for math and physics in school, and would often discuss and give feedback on other's work.

Hmm... so far so good.
Even though this has made me sort of a "go-to" person for any kind of help, I'm happy to do it because it helps me as much as the person I'm helping.

I think you can either cut a few words or edit a few things in this sentence. Be a little more assertive on your position. This sentence just sounded a bit weak to me.

At a local school for disabled children, many parents of children with communicative disabilities were unable to afford certain speech generating devices for their kids.

You don't have to do this edit. I personally thought it was slightly redundant but it does have a certain feel to it.
Looking at the devices, I knew that they had very simple soft- and hardware, and were clearly over-priced. It wouldn't be hard to write software that converts any desktop or tablet PC into a "Talker". I felt compelled to help them, and my father and I developed such a program, which is now being used in the whole school, free of charge.

ThisMy attitude is also a large part of why I want to attend MIT. I feel that with the opportunities MIT can provide me with, I will be able to truly have an impact on the world, and to make other people's lives better.

Overall, good essay. Just added a bit of minor edits and so forth. Those are just my personal opinions. It might not be the idea you wanted to convey, so don't feel obligated to change anything! I really enjoyed reading your prompt. Best of luck! ^^