As WMF's research efforts expand (great!), we're seeing more and more surveys. Some of those are being linked from MediaWiki itself, see for instance Qualtrics at T1005 and previously SurveyMonkey for MediaViewer.
Note that this matter is distinct from the questions 1) whether it's appropriate to use unfree software, 2) what software is statistically suitable, and 3) how multilingual they are/how good their i18n and integration with the [[https://www.mediawiki.org/wiki/Help:Extension:Translate|Translate extension]]. The discussion about that was at http://thread.gmane.org/gmane.org.wikimedia.analytics/345/
As for privacy:
- #WMF-Legal has vetted Qualtrics and it has gone through the Contracts team.
- LimeService seems rather good but should be verified. https://www.limeservice.com/en/pricing/21-english/general-content/39-data-protection-statement They don't need Safe Harbor because they already are in EU (with Canada option).
- Google Docs is sometimes used for events feedback etc. and by the community because it's very easy to set up, sometimes widely advertised e.g. [[https://id.wikipedia.org/w/index.php?title=Templat:AdvancedSiteNotices&oldid=9529424|id.wikipedia sitenotice]]. Privacy doesn't exist, it's the general "do whatever you want" Google policy.