There are a few and the more into engineering/CS type of fields the higher the scores you'll typically see. I know when I was applying most of the Ph.D. only programs I was looking at wanted scores in the 85% (which included both public and private schools, although 85% is slightly lower than 1400). In some programs having a high gpa/gre can make you elligible for university fellowships. Here are a couple examples from the web of scores close to 1400, but if the rest of your application is solid you wouldn't need scores in this range so don't focus on scores/GPA only, just apply and see what happens.
MIT Biology: "All interested students are encouraged to apply. The average undergraduate GPA for admitted students is 3.62, and the average GRE's are:
Verbal (650; 88%),
Quantitative (738; 87%), and
Analytical (735; 90%)."
UT Austin Biomedical Engineering:
"Applicants are required to have a degree in engineering or physics and expected to have a GPA of 3.75/4.00 in upper division or graduate coursework and GRE score of 1400 (verbal and quantitative)."