The online questionnaire tool Unipark, used for many psychological studies, features a progress bar to provide feedback to the participant. Not really a game element per se, but similiar in goal (engagement) and method (feedback) to many gamified applications.

http://www.unipark.info/1-0-online-befragungssoftware-fuer-studenten-und-universitaeten-unipark-home.htm

I remember that I also read about the use of Gamification in order to get better results out of surveys. If you just Google it you find many results:

http://enterprise-gamification.com/index.php/blog/3-examples/53-making-surveys-more-fun

However, most of these applications aim at market research and I can’t find results about psychological surveys.

When it comes to experiments and using Gamification in order to make experiments more appealing for participants, I think you also have to look at possible side effects. In general, you do not want to have effects of the Gamification on our experiment results (at least if the Gamification is not the aim of the experiment). Depending on the game mechanics used, the Gamification and thus the participation in the experiment might just be appealing for part of the population which you would actually like to examine. Therefore, you would not have a representative sample.

However, if you try this please let us know about your experience!

https://www.google.de/search?q=gamification+survey&pws=0&ie=utf-8&oe=utf-8&hl=de

You will find some very cool research stuff in the following

http://gamification-research.org/chi2013/

Here is a 1.5-year long field experiment on gamification:

http://gamification-research.org/2013/05/1-5-year-experiment-on-gamification-surprising-results/

and here is a psychometric study on social aspects of gamification:

http://gamification-research.org/2013/07/social-aspects/

plus a literature review on other empirical studies on gamification:

http://gamification-research.org/2013/09/does-gamification-work-a-look-into-research/