The answer, my friend, is 4Q.
There's two ways to survey your website visitors and analyze the data. One is to try and overcome all the challenges of web-based statistical surveys and try and learn things that may or may not be representative samples of what your web audience really thinks.
The problem with this is that every customer satisfaction expert (and me, who is not an expert) will tell you that your results will skew negative. In other words, people frustrated with your website will take your survey more often than those who are happy.
So, how about instead, just ask a random sample of your users a few questions and look for things that are broken or create unhappy users? Leave the "statistically significant surveys of your audience to someone who's got tens of thousands of extra dollars in their budget.
As an example, I recently spoke to a nonprofit about their donation checkout page. I said, "OMIGOD! It's three seperate screens to input shipping, billing, and credit card info until you can donate?!?!" (Yes, I use multiple exclamation points when I'm freaking out in real life)
They said, "Yes, we get lots of complaint email about that."
So they fixed it. The secret to good websites is to listen to your customers, not to ignore them because they don't represent a balance of all your users. I've had 4Q on my website since May and here's an example of the kind of reports you get:
4Q asks people the purpose of their visit and then whether or not they were able to accomplish that task. Further more, it can give you a nice breakdown about what people are coming to your website to do.
These results say, by the way, that I need to tweak the survey because the "other" category is too big.
This reinforces that. Also since I have a small web audience, you can see the small sample size.
You can also download Excel reports with the raw data.
[The photo of an entirely different kind of survey is from flickr user LukeOlsen]