How important are GRE scores for geoscience grad school?

I took the GREs twenty years ago this month. Twenty years! I spent an entire day of my Christmas break in a big lecture hall at the University of Maine, filling in bubbles with my #2 pencil.

The world has changed in the past twenty years. GREs are taken on computers these days, and the bizarre but fascinating logic problems are gone. ("Jenny likes cabbage, but Fred is allergic to horseradish. Who is seated beside Louise?") There's a new writing section, along with the verbal and math sections. And there's no longer a geology subject test. So I've become less and less capable of giving any kind of reasonable advice to students about how to prepare for it. And because I don't read grad student applications, I don't have any idea how grad schools look at the current version of the test.

When I started grad school, I got the impression that the GREs weren't particularly important for anything except competing for NSF graduate fellowships. Research is not a multiple choice exam, and the ability to fill in little bubbles (or whatever mouse-click has replaced it) is no substitute for creativity, perserverence, and the ability to take a lot of criticism. I've gotten the impression that the things that matter for a graduate application are 1) a coherent statement of purpose that fits with the research interests of a faculty member; 2) good grades in relevant coursework (maybe geo, maybe math or chemistry or physics); 3) strong letters of recommendation; and 4) maybe research experience, although it's become common enough at the undergraduate level that it might not mean as much these days unless it's incorporated into the statement of purpose. The GREs - well, the general test is taken by everyone, from physicists to literary scholars, and it would be hard to come up with a test that could identify people who would be skilled at both subjects. I remember the verbal section as being essentially the SATs with longer words (but not geology jargon), and the math section as being algebra. I took it, I sent off the scores, and I never thought about the test again*. Until students came to me worrying about it.

So here's my question to the rest of the world. Based on your experience, do GRE scores matter? Do some schools put more weight on them than others? Is there a minimum cutoff score for some schools, or are they used as a tie-breaker between otherwise similar applications? Or are they a form of practice at jumping through hoops, preparation for things like dissertation formatting instructions?

*Well, other than to score geek points against my soon-to-be-ex college boyfriend. But once I got to grad school, I didn't think about the scores.