Lawyers for the Summum religion had argued that its monument should be allowed in a public park where the Ten Commandments were already displayed.
The US Supreme Court rules in the case of an alleged drug dealer in Utah.
In a Massachusetts case, a kindergarten girl allegedly was sexually harassed by a third-grade boy on a school bus.
The decision will make it easier for local residents to recover damages from national firms, consumer groups say.
Its new term, which starts Monday, includes cases on detainees and TV language.
Five justices footnote their June opinion about a 'national consensus' against using the death penalty for child rapists.
The historic 5 to 4 ruling says the right to bear arms applies to individuals.