Please provide information on some criminal cases to do a report on.
It would be very helpful if you could provide more information with regard to the sort of assignment you are doing and what sort of cases you need. This would make it more likely that we could suggest appropriate cases.
For example, it may be that you are looking for cases that have to do with criminal justice and the process of investigating and trying criminal cases. If that is what you are looking for, there are many important cases. These include
Mapp v. Ohio, which applied the exclusionary rule to the states.
Gideon v. Wainwright, which established that defendants in state criminal trials have the right to an attorney even if they are too poor to afford one.
Kyllo v. United States, which established that police cannot use a thermal imaging device to detect excess heat (associated with growing marijuana) coming from a house unless they have a search warrant.
On the other hand, it may be that you want famous criminal trials, even if they did not hinge on or bring up any important points of law. A famous case that is relatively recent is the O. J. Simpson murder case. Another one that is much more recent is the prosecution of Gerry Sandusky for child abuse. Cases from long ago include the case of the kidnapping of the Lindbergh baby and the murders by Leopold and Loeb.
Please post a new Question to clarify the nature of what you need if you feel that would help.