I don't know all of them, but I would suggest GIA and AGS as the top 2 with EGL, IGI etc following up. Though some tout EGL US as having a similar strictness to GIA, it's really about preference. GIA sets most of the standards for which stones are graded/judged by.
I wouldn't focus too much on the certificate, if you find a great stone, get it appraised at an independent appraiser and they can tell you if it matches the cert and probably many many things that the cert does not say anyway. Some people on here have also gotten great deals without certification, and just had the stone appraised for confirmation.