According to Glenn L. Pace, Second Counselor in the Presiding Bishopric in the April 1989 General Conference:

A prophet doesn’t take a poll to see which way the wind of public opinion is blowing.

Here are the surveys the Church was performing previous to and those it has conducted following that statement:

note: I am merging lists, so it’s possible one or two of these is a duplicate of another (listed via a different source).

  1. 1963 “We are in the midst of a survey looking toward the possibility of admitting Negroes” here
  2. 1988 Temple Survey (Research and Evaluation Division) here or here
  3. 1991 Single Adults survey here
  4. 1999 Survey on less-actives (referenced in GC here)
  5. 2005–2013 Member Trends survey, see footnote #4 here
  6. Confidential LDS Church Survey, mostly regarding the LDS essays, March 14, 2014 here
  7. Survey on women, ordination, apostasy, and PR, 2014 here
  8. Survey on temple garments, officially linking to, and performed by Qualtrics. here, here, and here
  9. Focus groups to better understand how millenials think about controversial topics here
  10. Survey on controversial topics here
  11. Poll from the Presidency of the Seventy to monitor the impact of the focus on Sabbath day observance here
  12. A survey inquiring about members’ experiences visiting the Washington DC Temple Visitors’ Center. here
  13. A survey regarding the perceived influence of the LDS Church in Utah politics. here
  14. A survey on perceptions and attitudes regarding religion and spirituality. here and here, with questions.
  15. Member panel survey, September 2014 here
  16. Survey on technology usage 2015 here
  17. Survey on believs in Mormon Doctrine, and go see Meet the Mormons here
  18. Summary of survey on youth engagement with media from Jan 2016 here
  19. 2015 Youth Survey on media (seems similar to but somewhat distinct from the Jan 2016 summary?) here
  20. Survey on same sex issues, 2014 here
  21. Survey on the Sabbath, Aug 2015 here
  22. Church Service Mission Slogan Survey, Oct 2015 here
  23. Survey on single members’ concerns
  24. Mission age change focus group (anecdotal) here
  25. Survey on the new Gospel Topics essays, September 2014, here
  26. Survey on gays in the Church, Nov 2017, here
  27. Correlation Research Division Youth Survey on youth committment to and engagement in the church, 56 pages, 2018, here
  28. Survey on difficult topics, 2021, here

note: very small list originally shared here

acknowledgements: About 10 of these were taken from a list made by /u/japanesepiano, and other bullets were supplemented with some of their info. 1963 survey h/t No_Engineering; questions on perceptions and attitudes regarding religion and spirituality h/t Stuart98; 2018 Correlation survey h/t formermormer.