Sometimes. If officers are chasing someone who just committed a serious crime, they can go in after him/her - it's fresh pursuit, while a crime is happening.
If there is a good reason to believe someone is in a house, officers can force entry to arrest someone if their delay would allow escape or destruction of evidence. Entry can also be forced to save lives or rescue kidnap victims, where a delay could result in injury or death.
Necessary Times for Forced Entry
With an arrest warrant, officers can go into a person's house to get them if there is a reason to believe that the person is there. If there is a reason to believe a serious crime is in progress, officers can go in using necessary force in order to investigate and arrest the suspect. If there is no clear urgency to act immediately, officers need to get an arrest and/or a search warrant. If the police have a lawful right to enter and demand entry, you can be arrested for obstruction if you refuse or deny entry in any way.