In order to arrest someone without a warrant, a police officer has to have probable cause that an offense has occurred. The 4th Amendment protects citizens from unreasonable searches and seizures. Unless there has been a felony committed and the suspect is about to escape, then those protections prevent an officer from making an arrest without a warrant.
Probable cause is a very low burden for the officer. In most cases that is very easy for the officer to acquire. However, the District Attorney must prove that the citizen accused committed the offense beyond a reasonable doubt at trial in order to obtain a conviction. Just because someone is arrested for D.W.I. or Aggravated Assault with a Deadly Weapon or any other crime does not mean that they will be convicted.