Google made a difference when produced search results in less than second. While that required a lot of parallel processing, the results compensated for the trouble.
Some of the resource-intensive queries are those that include advanced operators (like site:, inurl:). Other factors are: personalized search, OneBox results or strange queries that require access to the supplemental index.
In 1999, the average search took approximately 3 seconds. Now most of the searches take less than 0.4 seconds. But I could find a simple query that took 4.22 seconds, admittedly for the second page of results. I wonder what was the problem (it was something temporary, if I repeat the search - it takes 0.28 seconds). Can you find other resource-intensive Google queries?