High fives to Wufoo, our long-time sponsor here on CSS-Tricks. It's powered the vast majority of forms I've built over the past decade. If you've never used it or heard of it: it's a form builder. It makes the arduous task of implementing forms trivially easy. Building a form on Wufoo means you'll get a form that does everything right UX-wise, gives you full design control, integrates with anything, and that you can put anywhere.
The feature list is too long to cover in the confines of a single post, so I always like to cover little bits that I've used recently and liked.
Don't forget they have a robust API. I used the API to submit form entries on a form just the other day. I wanted to do some special things on a form, like be able to react to the DOM event of submitting the form. That's not really possible when the form is in an <iframe>, but just fine when you host the form yourself and submit via API. Worked great.