No there are not, there are some instances where they can invoke probable cause but that is almost always when you are not home.  As to departments, don't start the stupid stuff like Game Wardens don't need a warrant, it is total BS.  

As to other nations, no we are NOT the only nation that requires a warrant for entry.   

 "Hot pursuit" is easily gamed 

 You have a perfect handle 

 You’re the only that are allowed to use deadly force to defend against unlawful entry though.