The discussion around the difficulty of providing such a list (and it's relative usefulness) is well summarized in Trey's notes from his research into the matter. 

https://www.mediawiki.org/wiki/User:TJones_(WMF)/Notes/Top_Unsuccessful_Search_Queries

On Wed, Aug 17, 2016 at 12:58 PM, Eran Rosenthal <eranroz89@gmail.com> wrote:
Unfortunately WMF policy to release search queries to the public is too strict.
(Although there are privacy concerns, I'm sure anyone here could easily think of some simple whitelist rules. For more details please refer to https://phabricator.wikimedia.org/T115085 or https://phabricator.wikimedia.org/T8373 or similar bugs in phabricator)

As a workaround you can use other data as approximation to what users look for (though you don't get the query itself, only the result - under assumption the users find what they look for):
https://wikimedia.org/api/rest_v1/ - page view data
or as dump:
https://dumps.wikimedia.org/other/analytics/

Other options (they have their own caveats but you can try):
* Search for "Special:Search/QUERY" in the pagecounts-all-sites linked above (zcat DUMP | grep "Search/") - this can provide you results such as "commons.m.m Special:Search/Jnnjjjnnnnjnjjnbnjbnjnjj 1 5418" so you know 1 user seared for "Jnnjjjnnnnjnjjnbnjbnjnjj" in mobile, at 2016-05-15 13:00-14:00
* Use google trends




On Wed, Aug 17, 2016 at 8:18 PM, Stas Malyshev <smalyshev@wikimedia.org> wrote:
Hi!

>> I’m currently writing by bachelor thesis at University Koblenz,
>> Germany. The goal is to improve Wikipedia search by exploiting the
>> text structure of Wikipedia articles. To conduct unbiased user
>> studies I need real world queries so I can compare the novel
>> algorithms agains the currently used ones. Are there any query logs
>> existing which I can use for this purpose?

We do have query logs, but they are not publicly accessible for privacy
reasons. You may want to check this out though:
https://meta.wikimedia.org/wiki/Research:Understanding_Wikidata_Queries

--
Stas Malyshev
smalyshev@wikimedia.org

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Yours,
Chris Koerner
Community Liaison - Discovery
Wikimedia Foundation