An ex-politician seeking re-election has asked to have links to an article about his behaviour in office removed.
A man convicted of possessing child abuse images has requested links to pages about his conviction to be wiped.
And a doctor wants negative reviews from patients removed from the results.
Google itself has not commented on the so-called right-to-be-forgotten ruling since it described the European Court of Justice judgement as being "disappointing".
Nor has it released any figures about the number of takedown requests received since Tuesday.
The original case was brought by a Spanish man who complained that an auction notice of his repossessed home on Google's search results had infringed his privacy.
The ruling surprised many because it contradicted the advice of the European Union's advocate general who said last year that search engines were not obliged to honour such requests.
EU Commissioner Viviane Reding described the decision as "a clear victory for the protection of personal data of Europeans" but others are concerned about the consequences that it will have for free speech.
Wikipedia founder Jimmy Wales has criticised the ruling, calling it "astonishing" while free speech advocates at The Index on Censorship said the court's ruling "should send chills down the spine of everyone in the European Union who believes in the crucial importance of free expression and freedom of information".
"The court has said that an individual's desires outweigh society's interest in the complete facts around incidents," it added.
Marc Dautlich, a lawyer at Pinsent Masons, said that search engines might find the new rules hard to implement.
"If they get an appreciable volume of requests what are they going to do? Set up an entire industry sifting through the paperwork?" he asked.
"I can't say what they will do but if I was them I would say no and tell the individual to contact the Information Commissioner's Office."
Although the judgement refers specifically to search engines and states that only the links to information, rather than the information itself, be removed from the net, some news organisations have seen a rise in the number of people asking to have articles removed since the ruling.