A perfect crime is a crime so well-committed that no evidence is left, and no solution by the police is possible.
The case of Leopold and Loeb is an American case that was almost a perfect crime, but a small detail botched it, and both perpetrators landed in prison.
Would-be perfect crimes are a popular subject in the movies, and many have been made. A few include Double Indemnity, The Postman Always Rings Twice, Witness for the Prosecution, and Dial M for Murder.
Note that many perfect crimes may have been committed, if there were no public or media knowledge of them. It should also be noted that police are fallible, and some never-solved crimes would have been solved, if the police had better resources at their disposal. In the well-known case of Jack the Ripper, evidence was left, but the crimes were never solved.
Some crimes such as the Tylenol scare of 1982 and the Diane Suzuki case of 1985 are referred to as perfect, but a possibility always remains that a culprit will ultimately be identified.