I recently needed to have an online form for people to register for next year's cookery classes here and I decided to use EMailMeForm.
It's a free service and offers customizable web forms ( Contact forms, online Questionnaires and Surveys ) and they host it on their server, so it works with any site, regardless of the ability to run scripts. I found it really easy to set up - I'm a non-techie! - and they also use Captcha to block spam.
You set up the fields that you need for your form and then copy the HTML code and paste it onto your site. When people fill it in they don't need to leave the site and they are directed to a page of your choosing which acknowledges that it has been sent and thanks them.
With the one account you can have forms on several sites.
As I said, I found it really easy to set up and ... it's free!