A warrant is based on "probable cause" of either criminal activity or contraband at a place to be searched. If convinced the judge will issue and sign a search warrant--a court order that authorizes police to search a location like your house for specified objects at a time specified. For the police, there are four main circumstances that a warrant is not required to search your house. (A search warrant is a judicial document that authorizes police officers to search a person or place to obtain evidence for presentation in criminal prosecutions.)
Doctrine of plain view.
If a policeman already has the right to be on your property and sees contraband or evidence of a crime that is clearly visible, that object may be seized and may lawfully be used as evidence. As but one example, if the police are in your house on a domestic violence call and see a lot of drug paraphernalia on the windowsill, those items can be seized as evidence.
Search incident to arrest.
If you are in the process of being arrested in your house, police officers may search for weapons or to find any other accomplices to protect their safety (also known as "protective sweep"), or the police may search to prevent your destruction of evidence.
If the person in control of the property consents to the search without being coerced or forced, a search of the house without a warrant is valid. Police do not have to tell you that you have the right to refuse a search. You do have that right. The Supreme Court recently ruled that one spouse cannot consent to the search of a house on behalf of the other spouse.
Exigent circumstances search.
This refers to emergency situations. It is thought that if the process of getting a valid search warrant could compromise public safety or could lead to a loss of evidence a search can go ahead. This situation encompasses "hot pursuit" in which a suspect is fleeing police and is about to escape. A recent Illinois Appellate Court decision ruled that police officers may enter a DUI suspect's home without a warrant on the theory that important evidence, namely the suspect's blood alcohol level, may be lost otherwise.
You'll need a lawyer to challenge a warrantless search of your house.