It would be helpful if you could give us some idea as to why you need these cases and what sort of assignment you are doing. This would help us understand what sort of case would best fit your needs.
Any case in which no one is being accused of a crime can be seen as a civil case. In a civil case, one side is saying that something wrong has been done to them or that some improper condition exists, but that these actions or conditions are not criminal. There have been many famous cases of this sort.
United States v. Nixon was one such case. In that case, the US government wanted to compel President Nixon to turn over tapes to the government. Nixon claimed executive privilege, saying he did not have to turn the tapes over because he was president. The Supreme Court ordered Nixon to turn the tapes over.
Bush v. Gore was a case that had to do with the 2000 presidential election. In that case, the dispute centered on whether Florida could keep recounting ballots that had been cast in the election. Bush ended up winning the case and becoming president.
Please post a new Question to clarify the sorts of things you need if you feel it would help.