The Fourth Amendment and Warrants
The Fourth Amendment says that people have the right to be secure against unreasonable search and seizure, and that no warrant shall issue but on probable cause and specifying the place to be searched and the persons or things to be seized. This means that an officer can only search or seize a person or their property with a valid search warrant, a valid arrest warrant, or a belief rising to the level of "probable cause" that an individual has committed a crime. Evidence acquired without one of these three conditions being fulfilled would be excluded from trial.
Probable Cause
The standard for conducting a warrantless search, probable cause, is the same standard necessary for a warrant to issue. Probable cause for arrest exists when facts and circumstances within the police officer's knowledge would lead a reasonable person to believe that the suspect has committed, is committing, or is about to commit a crime. Probable cause has to come from specific facts and circumstances, not simply an officer's hunch, feeling, or suspicion.
Probable cause for a search exists when facts and circumstances known to the officer provide a basis for a reasonable person to believe that a crime was committed at the place to be searched, or that evidence of a crime exists at the location.
Probable cause to seize property exists when facts and circumstances known to the officer would lead a reasonable person to believe that the item is contraband, stolen, or constitutes evidence of a crime.
Search and Seizure
There are a number of circumstances in which an officer can conduct a search, make an arrest, or seize items without implicating the Fourth Amendment and probable cause concerns.
The police can conduct searches where necessary to ensure their safety and the safety of the public. Objects that are in plain view such as a bag of drugs in the backseat of a car do not require a warrant or probable cause to be seized and admitted as evidence. In an emergency the police may conduct a search; an example would be while in pursuit of an armed fugitive. Searches of an individual and the surrounding area are permitted when an arrest is conducted. Finally, if consent is given no warrant or probable cause is necessary to conduct a search.
In addition to these circumstances someone in charge of a space, such as a roommate or spouse, can give consent for your home to be searched. A car that has been towed and impounded may be searched. An officer can pat you down during many kinds of stops, though this is limited to a search for weapons.
In short, there are many circumstances in which the police may search and seize you or your possessions even without a warrant or probable cause. If you were subject to a warrantless search it is important to recall the details of the events leading up to the search and review them with an attorney to determine whether your rights have been violated.