California vs. Greenwood was a Supreme Court case in 1988, and dealt with the effect of the Fourth Amendment on warrantless search of garbage left on the curb. Billy Greenwood was suspected of dealing drugs, and police searched his garbage; evidence found there led to a warrant on his house and the discovery of more drugs inside. Greenwood argued that searching his garbage violated his rights under the Fourth Amendment, requiring a warrant to prevent unlawful search; after winning the case in California Superior Court, the decision was reversed by the Supreme Court, who ruled that garbage placed on the curb has no reasonable expectation of privacy.
There are a lot of sources online for this case; if you or your school has a LexixNexis account, the full case can be viewed here. Wikipedia has a short summary of the case, and Wikisource has some more information. The sources linked below also have a lot of information, some of which is obscure unless you have a strong understanding of U.S. law.
The brief summary would be as follows: Police are informed that Billy Greenwood is dealing drugs; police search Greenwood's garbage; police obtain a warrant and find drugs in Greenwood's house; Greenwood fights the case and wins in California; the Supreme Court overturns the decision.