If I have a warrant out for my arrest can the police come into my house and arrest me without a search warrant?
Generally, the police cannot arrest a person in their own home or private residence without an arrest warrant. The 5th Amendment to the constitution states that citizens shall be protected against unreasonable "search and seizure". This protection extends to the right of persons not to be arrested in their home without an arrest warrant. Exceptions to needing an arrest warrant would be for cases when the police are in "hot pursuit" of an individual they suspect has committed a crime and that person enters a private residence. Police can also make an arrest without an arrest warrant to protect others from immediate danger, to prevent the destruction of evidence, or when contraband is in plain view. People can also be arrested without an arrest warrant for a variety of traffic related offenses.
When an arrest warrant is required to make an arrest, the arresting officers must show the arrest warrant to the person at the time of arrest (or shortly thereafter). The only time an officer does not need to show an arrest warrant is when they reasonably believe that doing so would threaten their safety, the evidence, or cause a suspect to flee.
When the police have obtained an arrest warrant they have been given the authority to enter a private residence and arrest a specific suspect. When a person is legally arrested, the police have the right to conduct a search of the person and their immediate area. If an arrest is made unlawfully any incriminating evidence obtained may later be deemed inadmissible in a court. Since this is a highly technical area of the law, you should consider consulting directly with a criminal law attorney.