Which case established the precedent that searches conducted without warrants may still be valid?

The case that established the precedent allowing searches conducted without warrants to be valid in certain circumstances is South Dakota v. Opperman. This case addressed the concept of "inventory searches," where law enforcement may conduct a search without a warrant when they lawfully impound a vehicle. The Supreme Court ruled that these inventory searches are reasonable under the Fourth Amendment as they serve a legitimate purpose: protecting the owner’s property, ensuring that the police do not claim any of it as their own, and protecting the police against false claims of theft.

This decision underscores that certain exceptions to the warrant requirement exist, particularly in the interest of maintaining safety and order, making such searches constitutionally permissible. The context of the case illustrates the balancing act between individual rights and the needs of law enforcement, leading to the conclusion that under specific circumstances, warrantless searches can be considered valid.