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As many of you know, Google is very unlikely to remove results from the search results. Time after time, Google has gone to lengths to explain why they do not like to remove search results.
That being said, there are times Google will remove search results.
As Daniel Roofer from the UK wrote very well in the Google Web Search Help forums, Google will remove content under the following circumstances.
1) Child Porn - click here for more information.
2) Social security number in search results - click here for more information.
3) Credit/bank card in search results - click here for more information.
4) Image of hand written signature - click here for more information.
5) My full name on a spammy porn page in search results - click here for more information.
6) By a court order or wish to request a legal removal - click here for more information.
7) Copyright infringement - click here for the DMCA policy.
8) Search Spam in Google search results here - click here for more information.
Of course, Google has an official document on this topic.
Forum discussion at Google Web Search Help.
