Whether you are writing about failure or one of the other essay options, keep in mind the primary purpose of the essay: the college wants to get to know you better. On a certain level, your essay isn't really about your failure. Rather, it is about your personality and character. In the long run, were you able to handle your failure in a positive way? Colleges that ask for an essay have holistic admissions , so they are looking at the whole applicant, not just SAT scores and grades . By the time they finish reading your essay, the admissions folks should feel that you are the type of person who will succeed in college and make a positive contribution to the campus community. So before you hit the submit button on the Common Application, make sure your essay paints a portrait of you that makes a positive impression. If you blame your failure on others, or if you seem to have learned nothing from your failure, the college may very well decide that you don't have a place in the campus community.
Some applicants may ramble on about themselves in a manner that may appear self-indulgent and not very appealing to the committee. Remember, this is an application essay, not an autobiography. Conversely, some applicants tend to say too little, perhaps hesitating to promote themselves too explicitly or not knowing what about themselves would be interesting to people whom they don't know. In such cases, perhaps focusing more on what you want to do than on what you have already done (let your record speak for itself) may help in getting beyond self-inhibition.