As William Shakespeare so wisely pointed out, being concise is critical for good writing.
I've been editing a lot of personal statements over the last few months, and I deliberately recommend a word count of 750 or fewer for my advisees for a couple of reasons:
First, I've found that that number is just the right balance of content and streamlining: Over 750 words for an admissions essay lends itself to meandering writing.
Second, your reader is likely reviewing tens or even scores of applications in a short period of time. S/he is looking to spend as little time as possible on your written materials, while still getting a good flavor for your candidacy. Don't burden your reader with verbiage.
Having trouble being brief? Here's a helpful trick: Imagine AMCAS, AACOMAS, or ERAS is charging you $10 per word. How would you keep costs down?