Most famously, suspicions of "cowboy" antics by police proved fatal for the prosecution in the murder-trial against OJ Simpson. Evidence was introduced of LAPD officer Mark Fuhrman being a hard-nosed racist and violator of Civil Rights, who talked of routinely committing and covering up police brutality and other police-crimes against citizens — particuarly African-Americans. Even though Fuhrman claimed that he was only playing a character for dramatic purposes, his proven use of racist language and innuendo allowed Simpson's defense-lawyers to create reasonable doubt into the minds of a jury, on an otherwise-strong case.
The "Rodney King" video likewise presented an image in the minds of America, of (white) "cowboy cops" beating a helpless (black) citizen; even though defense-lawyers successfully argued that that the police were going strictly "by the book" in properly subduing Mr. King as a criminal suspect, their acquittal resulted in the famous L.A. Riots, and sparked the officers' eventual conviction on Civil Rights charges.
The London Metropolitan Police have been accused of slipping into this territory recently, among other things they've tried to engineer the dismissal of a government official, and recently it's been reported that after questioning gang members they've been dropping them off in territory controlled by rival gangs, which is sometimes tantamount to a death sentence. They've also been accused of using excessive force against peaceful protests, partially good old fashioned Police Brutality, and partially the controversial "kettling" technique. Not to mention the standard racist and anti-Islamic behaviour when dealing with minority suspects, and infiltrating any political group that criticises them or campaigns for internal investigations into their behavior.
Maricopa County, Arizona sheriff Joe Arpaio is what happens when a Cowboy Cop becomes Da Chief. He promotes himself as "America's Toughest Sheriff", takes a very hard line on crime (especially illegal immigration, often to the detriment of other enforcement), and his handling of the prison system has included: making prisoners wear pink underwear, bringing back chain gangs (albeit volunteer-only), creating a tent city to house surplus inmates (both prisoners, and those merely awaiting trial) outside in the Arizona heat (justifying it by claiming that American soldiers in Iraq wearing body armor live in the same conditions, which they don't), setting up an in-house radio station called "KJOE" (playing classical music, opera, Frank Sinatra and patriotic music), and being called out twice by the federal courts for violating Constitutional provisions against cruel and unusual punishment (including charges of feeding moldy, spoiled food to prisoners and denying medical care. Furthermore, he operates a county jail, not a pennitentary or state prison, meaning many of the people sent to him are not convicted of a crime yet).
Property destruction, too. He once brought a full SWAT team complete with tank to break up a cockfight. Why such a show of force? He swears it had nothing to do with the fact that Steven Seagal was filming an episode of his TV show with them...
Christopher Dorner was a strange subversion of the usual order. While he hated the LAPD's structure and regulations and was described as a Loose Cannon by superiors, his conflict with them was for completely different reasons than usual — he thought that the LAPD was covering up out-of-control Police Brutality and racism, and felt that his attempts to expose this were the reason he got fired. It ultimately ended in him Going Postal, killing four people before barricading himself in a cabin at Big Bear Lake, where he died after an extended siege.