Is it possible to sort Google Search results by popularity for a given search term? Also, is it possible to sort results by popularity for a specific website (e. g., Wikipedia)?
Google's search results are sorted by relevancy. The most relevant search results for the user are at the top. Google uses over 200 factors to determine the relevancy. Pure "popularity" might well be one of these factors, but there is no way to directly change the order of these results.
(Aside: But what is "popularity"? Is it the number of times web pages are visited (perhaps determined by analytics)? The number of times webpages are clicked on in the SERPs? The number of inbound links to that website? That last one is certainly one of the most important factors that Google uses - so in a sense "popularity" is already strongly linked to relevance.)
To search in a specific website, use the