I'd like to add a survey to a website. I'd like to use a service like survey monkey. However, I'd like to send some kind of REST or SOAP call instead of redirecting my users to their website.
Survey Gizmo is also a very nice service, with some really great features that Survey Monkey doesn't have. It's generally more expensive though.
Lastly, if you're looking for a FLOSS option, you could check out Survey Project for a DIY approach. It's free (beer & speech), but you'll have to host your own database underneath it and your maintenance cost will be greater. Don't forget that FLOSS is never free as in beer, it's free as in puppy.