To the chagrin of many applicants, the Common Application and many other college applications do not provide guidelines for formatting personal essays. Should the essay be single-spaced so that it fits on a page? Should it be double-spaced so it's easier to read? Or should it be somewhere in the middle, like 1.5 spacing?
The bottom line is that either single- or double-spacing is fine. Many college applications don't provide spacing guidelines because the admissions folks truly don't care what spacing you use, and many applications that do address spacing say that the essay can be single-or double-spaced.
However, the few colleges that do specify a preference typically request double-spacing. Also, if you read the blogs and FAQs written by college admissions officers, you'll usually find a general preference for double-spacing.
There are reasons why double-spacing is the standard for the essays you write in high school and college: double-spacing is easier to read quickly because the lines don't blur together; also, double-spacing gives your reader room to write comments on your essay (and yes, some admissions officers do put comments on essays for later reference).
So while single-spacing is fine, my advice is to double-space. The admissions folks read hundreds or thousands of essays, and you'll be doing their eyes a favor by double-spacing.
A final formatting note: always use a standard, easily readable 12-point font. Never use a script, hand-writing, colored, or other decorative font.