How to stand out in math graduate school admissions
Consider the viewpoint of the admissions committee. How would they know who to pick? One way is to trust others opinions -- this is why they seek recommendation letters from those who know your abilities. 

If you still want to "stand out", and aren't satisfied with your performance in the standard ways (grades, exams, REU programs), consider what makes you different. You should seek advice from those who know you better than us for ideas here.

In addition, if you're afraid of not getting in anywhere -- apply to a spectrum of schools, and simply pick the top one(s) you are accepted to. Having backups is a good way to be safe.