Poll:
Easy-Poll.com let you quickly and easily add a poll to your website. They store the results and you manage the poll through your account with them. Although you lose some control over the poll having all information passed to them, this is a drop-dead easy solution for the non-developers out there.
http://www.easy-poll.com

Survey:
LimeSurvey is probably the best open-source, PHP, survey script I have found. Its highly customizable and can handle most kinds of surveys you want to put up with ease. The down side, and there is always a down side, the admin area is kinda confusing and non-intuitive to use. Once you get past the admin area you will probably find that LimeSurvey works great. (oh and they have a very nicely designed website)
http://www.limesurvey.org/

List of more surveys:
http://…/Onlinesurveys/software.htm#freesoftware

Check out these posts too:

  1. 10 Steps To Protect The Admin Area In WordPress
  2. PHP script to manage online surveys
  3. Test your website in IE6, 7 and 8 with SuperPreview
  4. Online surveys made easy with Zoomerang
  5. Free newsletter manager for your website
  6. Three tips to protect your WordPress installation from Matt Cutts
  7. Wufoo · Making forms easy + fast + fun.