Google received more than 345 million requests to remove links to copyrighted material last year - up from just 62 in 2008.
The UK music industry trade body BPI appealed most to Google, asking for more than 60 million links to be deleted from its search index.
Just three sites accounted for five million of the URL takedown requests - uploaded.net, 4shared.com and rapidgator.net.
The figures were compiled by Torrent Freak using Google's weekly transparency reports. The majority of copyright takedown requests to Google are complied with.
But in its annual piracy report, Google said the reason some people turn to illegal content is because it is difficult or too expensive to obtain it legitimately.
It said: "Piracy often arises when consumer demand goes unmet by legitimate supply.
"As services ranging from Netflix to Spotify to iTunes have demonstrated, the best way to combat piracy is with better and more convenient legitimate services.
"The right combination of price, convenience, and inventory will do far more to reduce piracy than enforcement can."
But the search company cited some example of where its free piracy link removal service had been abused.
It said a driving school in the UK asked for a competitor's homepage to be removed from Google Search, because it had copied a list of cities and regions where tuition was offered.
Meanwhile a company in the US requested the removal of search results that linked to an employee's blog post about unfair treatment at work.
Both of the requests were refused.