Recruiting season is winding down, and I have been thinking about GMP's post on the topic from a week or so ago. As I said in my comment, I find prior research experience to be the most important consideration for me. Students with no exposure to research have no real idea what it is like, and can therefore easily not understand what they are getting into in grad school. Also, sometimes people just have really bad hands in the lab, and would be better served with a less hands on group than mine.
In my experience, grades are actually a poor predictor of success (once above a certain minimum threshold of competence). I need to know my students can pass our grad level courses required for their program, and grades are a good predictor for this. I've found that many students with high GPAs are not necessarily good at research. Some of them are profoundly disturbed that there may not be a "correct" answer to their research problem (happened to a friend of mine). Others are good at schoolwork, but not so good at applying that knowledge to the real world. Some are brilliant at everything including research, and these are the ones I want! High GPA does make it easier to get fellowships, so I am happy to attract 4.0 students, of course, but I don't accept students on GPA alone, nor do I use GPA as a filter. My best students right now were closer to 3.0 then 4.0 as undergrads.
I do look for a GPA trending up with time if the GPA is on the low end of our admitted pool. This is often a sign that a student has put it together in terms of figuring out how to work/learn/understand some key concept that eluded them the first time around, but may disqualify them from "better" programs. I don't consider students with a significantly downward trending GPA unless they are super excited about my research and have kick ass research experience and letters. I don't look at GRE scores that much either, other than to make sure they are adequate. I prefer students with good verbal scores, since writing is a big part of what we do, and this is harder to probe in a meeting.