On Stack Overflow, it's ... [agile]. Well, at least if you look at tags which are used 1000 times or more, of which there are ~4000. 48% of the questions tagged [agile] have been downvoted. Not surprising, since it's considered off-topic.
I found it with this query. It's easier to count questions which aren't downvoted, and combine it with the denormalized
Tags.Count column which tells you how many questions there are in total.
For reference, here is the complete query:
t.[Count] AS '# of questions',
ROUND(100.0 * (t.[Count] - COUNT(*)) / t.[Count], 2) AS '% downvoted'
FROM Tags AS t
INNER JOIN PostTags AS pt ON t.Id = pt.TagId
LEFT OUTER JOIN Votes AS v ON v.PostId = pt.PostId
AND v.VoteTypeId = 3 -- downvotes
WHERE t.[Count] >= ##MinTagCount:int?1000##
AND v.PostId IS NULL -- so we select the questions WITHOUT downvotes
GROUP BY t.TagName, t.[Count]
ORDER BY ROUND(100.0 * (t.[Count] - COUNT(*)) / t.[Count], 2) DESC
Bonus result: the 2nd highest downvoted tag on Meta Stack Exchange is ... wait for it ... down-votes with 69.25%.
I realize that a tag where all questions have been downvoted (100%) would not appear in the query results. I think it's safe to assume that given the >1000 filter, we're not missing any tags.