I think that certain times call for different rules of engagement, I think that sometimes the US has had a very robust ROE, I can recall watching a documentary called "The Ghosts of Abu Ghraib" - there was one scene in that film which shocked me. The film makers were interviewing a former rear gunner of a Chinook - he told them that he asked his CO and squad members what were the rules of engagement, their response was "If it looks like the enemy, shoot it." That really blew my mind. Really? "If it looks like the enemy, shoot it."?
That being said, there was controversy in Northern Ireland surrounding a so-called "Shoot to Kill" policy, where British Army and Special Forces soldiers had supposedly been given orders to shoot to kill the IRA, rather than arrest them.
Firstly, these are Special Forces, not squaddies - at the point when they are brought in, they're not there to arrest terrorists (although one exception would have been the Peterhead Prison siege.)
Secondly, there was a massively controversial issue again in Gibraltar in the 1988 (Operation Flavius), the SAS was sent in to arrest a Provisional Irish Republican Army (PIRA) cell, thereby stopping them from attacking the Changing of the Guard ceremony at the Governor's Residence on The Rock. Their targets were Danny McCann, Sean Savage and Mairead Farrel. Their orders regarding engagement were thus: "Open fire against a person [only] if you or they have reasonable grounds for believing that he/she is currently committing, or is about to commit, an action which endangers your or their lives, or the life of any other person, and if there is no other way to prevent this.
The SAS were observing their targets, actually by walking behind them. When they saw that McCann was making an aggressive move toward a bag that he was carrying, they killed him. At that moment, they also saw that Mairead Farrel was reaching for something in her handbag, she too was killed. The third man, Sean Savage, made a move for something in his pocket - he too was shot and killed.
These are just two examples of the rules of engagement and how right, or wrong they might be. Heading back to America and their military's ROE... I read an article in the BBC not too long ago, which talked about a US Kill Team, which went around targeting persons, that is a MASSIVE breakdown in the Chain of Command, not to mention that it makes the US military look like a bunch of 'Yee-Ha-Oops' cowboys.
Anyway, I completely agree with KJ's assessment of Rules of Engagement.