If you want to record video directly from your website there aren't many options I could find.
Here are the only two I have found so far:
I may be missing some obvious one because I find hard to believe there are no major players on this field.
The reason could be that there is not a high demand for what you are asking for.
Most video recording from web is done via YouTube or Facebook which have really nice integrations of the Flash video recorder.
I don't think it would be practical to refer potential customers to another site and take the time to record themselves to give you feedback.
Also, I don't see how that would be so much more valuable than just plain written feedback like the one you can get using the now popular GetSatisfaction or UserVoice sites, or just a contact or feedback form on your site.
If you really need to see people faces testing your product I would recommend Usertesting.com which is a way to run usability testing over the web for $29 per 15 minute test. The test session is recorded with a screencast (audio + video) and it is a great way to learn how your customers interact with your product.
However, If there is not a real reason to be able to see your customer faces I would strongly recommend to stick with written feedback.
I have developed http://userlove.net for this.
You can see an example here: http://userlove.net/products/7 Contact me at aymeric[at]wiselabs.net if you want to have access to the tool.
There are a couple of sites I know of that offer this type of service: