<p>Nothing is ever absolutely necessary, but a complete lack of research experience is a problem that most people could not overcome in “top” grad admissions. The problem is that many people who excel in classwork fail at (or hate) research, and if you have no experience at it neither you nor they can be sure how you will handle it. You can overcome that by being far superior in other areas compared to the rest of the candidates, but that generally takes you out of the top programs - you would have to apply to a mid-range program (at best) to have a chance to so overshadow your competition.</p>
<p>However, REU is not the only research option. Check with professors in your department about work available in their labs - with a 3.70 gpa you should be an attractive candidate. They might not have funding to pay you (but you can hope!), but you’ll get experience. For that matter, a year working under a professor part-time during the school year may be a better resume boost than a single summer in an REU.</p>