It's funny about the GRE. High quantitative scores are apparently much more common than high verbal scores. According to this table published by ETS, "seniors and non-enrolled college graduates" have scored as low as 740 verbal and still been in the 99th percentile, but enough have gotten an 800 quant to make it only 95th percentile.1 That makes it kind of hard to get the "percentiles in the high 90s" that, for instance, Stanford says they're looking for.
Ye olde U.S. News rankings paint a similar picture. It'd be nice if they published info about CS departments specifically, but apparently they don't, at least not for free. They do publish it about engineering grad schools, though. Stanford: 569 verbal, 778 quant; UCSD: 542 verbal, 764 quant; Washington: 537 verbal, 733 quant.
What's with the huge discrepancy in verbal and quant scores? I'm sure part of it is that tons of the applicants to these programs are international students who just aren't fluent in English, at least not according to the GRE. I'd be curious to know what the breakdown is for applicants for whom English is a first language, though. If computer science is full of smart people who nevertheless have trouble expressing themselves clearly and precisely in written English, it seems to me that we're in trouble. When smart people can't write, they sometimes embellish and obfuscate in an effort to make their writing seem better, which is an especially bad thing to do when you're writing a proof, for cryin' out loud.
Why is the math score so high? The kind of math the GRE tests doesn't really seem to be the kind of math that computer science calls for. I think that it's possible to be a competent CS grad student without being great at that kind of math. And yet, if the scores are to be believed, most CS folks are great at that kind of math. Is that a side effect of having gotten as far as they have in CS? I didn't know I was into it until halfway through undergrad, so maybe I didn't experience the side effect.
Actually, I wonder if maybe the whole GRE tests for a side effect! That is, doing well on the GRE is a side effect of being smart, but we don't have a metric for "smart", so the GRE is a stand-in for that -- which is unfortunate for anyone who managed to miss out on the side effect for whatever reason.