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 Translate extension. The discussion about that was at http://thread.gmane.org/gmane.org.wikimedia.analytics/345/
Services used by WMF
- https://wikimedia.qualtrics.com/ has been vetted by WMF-Legal and it has gone through the Contracts team.
- http://www.allourideas.org/ has been vetted by WMF-Legal.
Not recommended but allowed
Not evaluated by the Wikimedia Foundation yet
- 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).
- https://opendatakit.org/ - self-hosted and cloud services available, including free for limited purposes (see http://www.kobotoolbox.org/#getstarted). An OSM integrated edition exists, by HOTOSM. Has Android app for offline collection. French Host of ODK derived solution: http://makina-corpus.com/realisations/application-mobile-makina-collect-nouvelle-version . More info about other ODK derivatives: http://carnet-terrain-electronique.fr/open-data-kit-odk/