It depends on the field you're applying for and how much they need a certain type of grad student.
If you're in the U.S., you're much less likely to be accepted into a top school if you are applying as a theoretical science (or biology), simply because of competition overseas where they cannot afford the expensive laboratory equipment that we can. They simulate everything, so they will in all likeliness have much more experience than you.
On the other hand, you can differentiate yourself through experience from good research programs and letters of recommendation from reputable principal investigators (people in charge of research).
If a certain field does not have as much funding, such as various soft sciences, it is also less likely that the school will want/need you.
If you maintain above a 3.5-3.6 GPA, that should be a relative safe zone as far as immediate rejection goes from schools like MIT.
Try to network and work under at least 2 but preferably 3 different P.I.s, one being a professor at your school, and 2 at REUs.
GREs aren't too important, but you shouldn't tank it. Here's a point of comparison:
1380 GRE/5.0 Analytical writing (49th percentile Chem GRE lol)
Various Chemistry awards
1 Letter of recommendation from a German professor during a DAAD-RISE research experience
1 Letter of recommendation from an NAS member
1 Letter of recommendation from school professor who is a Harvard PhD alumni
And this student was accepted into Harvard grad school for Chemical Physics (along with MIT, Stanford, and Caltech).
He's a very sociable and friendly guy, but he calls himself a moron albeit being accepted into almost all of the top 5 schools. I don't think he was anywhere near being the top ranker at his school (UCI).
As he's told me, most of your competition will be partying on the weekends. That's when you need to be studying.
There was a guy from my school last year who got into the comp sci PhD at MIT. I have no idea what his class rank was (I'm not even sure if my school does class rankings...I've never seen them), but he was a fantastic student. He was a double major and I have to imagine he was the best student in his year in both depts. He did honors and everything.