Here's a quick way to estimate your odds of getting into a business school. Take it for what it's worth...
First, assume you're an average applicant. In reality you aren't average, but I don't have a way to adjust for your GMAT score, your undergraduate GPA, your experiences, the adcom's mood, or any of the variables that could influence the outcome. So assume you're Joe Average.
Next, look at your odds of getting in to one of the top schools - HBS for example. Last year, HBS admitted 15% of its applicants. So say that's your chance of getting in to a top school.
Last, use the binomial distribution to calculate the odds of getting into 1 or more schools, assuming your chances of getting into any of the schools is .15. Here's what you end up with:
Using this estimate, if you're an "average" candidate and you apply to four schools, there's a ~50% chance you'll get into one of them.
Yes, there's a problem with this approach, namely that it assumes each application is unrelated to the others. Clearly that isn't the case, since your applications all have one important thing in common: you. If you are accepted into HBS, chances are your application is strong enough to get you into other schools as well. And if your application is weak, applying to a lot of top schools isn't going to improve your odds very much. So your odds of admission to each school you apply to are correlated, not independent.
Still, I think this is useful for deciding how many applications to send in. Four to six seems about right; after that you start seeing diminishing returns.