Typically, misdemeanor crimes do not involve an arrest, and they do not involve a "breach of the peace," meaning nobody is injured or disturbed in any malicious way. There are some exceptions... in many states, possession of small amounts of marijuana is considered a misdemeanor offense, where you generally won't spend time in jail, but may be officially "arrested" for the record. Minor traffic crimes have long been considered unarrestable offenses, but a 5-4 decision by the United States Supreme Court has set the precedent for which law enforcement can decide whether or not to arrest somebody.
The case involved a woman who was driving without her seat belt (along with her two unbuckled kids). She was pulled over and didn't have her driver's license and proof of insurance (her purse had been stolen the day before), so she was arrested and released on bail for $310. David Souter, one of the most liberal members of the court, was on the side of the state, as were the four Conservatives -- Clarence Thomas, William Rehnquist, Antonin Scalia, and Anthony Kennedy.
In general, a crime must involve a "breach of the peace" in order to be an arrestable offense. This has long been considered common law meaning that unless violence of some sort is involved, law enforcement will tread lightly. In refuting this common law idea, Souter pointed out the fact that British Parliament (before the founding of the US) allowed arrests for many simple offenses, such as "night walking", cursing, and negligent carriage driving. How this is supposed to make it clear why America should allow such arrests is beyond me.
The director of The Cato Institute (a Libertarian think tank), Timothy Lynch, had the best comment on the situation that I've found so far: "The Framers of our Constitution would frankly be startled by the Supreme Court's cavalier treatment of the legal threshold by which citizens can be deprived of their liberty and thrown in jail."