If you want it to be available on every page, you might want to consider using jQuery and the UI Dialog plugin. You could set it up so that the default feedback is a mailto which gets replaced using javascript with a link that brings up a jQuery Dialog containing the fields you want to collect. This could be submitted back to your server via AJAX and delivered to you via email from the server.
EDIT: Since you've edited your question to indicate a server-side only solution, the above seems somewhat out of context. With others, I would agree that using some client-side code to actually send the email is the way to go (as alluded to above). I think it's preferable to use your own server for this, but I'm sure that you can find many "form to email" services. I would avoid these, unless you want your email addresses harvested for use in SPAM. You might also be able to use a signed applet or ActiveX control for this, again I would not go down that route. As indicated above, I would let the browser handle the interface, but my server handle the sending of the email.