Define harass.... did they detain you? Did they ask you a few questions and then went about their business? Did they make you leave the public place?

I'm not trying to tick anyone off but law enforcement tends to be in a damned if they do and damned if they don't position. If they don't follow up with due diligence and someplace gets bombed then they get bashed for not doing their jobs. If they do follow up on "suspicious activity" they get bashed for harassment...

Be polite, talk openly to them with the respect they deserve and you shouldn't be harassed at all... but that depends on your definition of harassment...

While all you cop bashers are salivating, I would like to give you another thing to think about. Maybe, just maybe, the cops don't like video and picture taking because it is an officer safety issue. Bad guys have been shown, in studies, to study video and stills which depict coppers doing their job, to see see if their training or responses leave them open and vulnerable in any way. While I'm at it, something cop bashers don't like to hear is that less than 1 percent of all officers tarnish the badge with poor behavior - that is a better stat than people of the Clergy. So go photograph something you know something about and leave the cops alone to do their jobs.

As a former Deputy Sheriff who worked the Traffic Unit, writing tickets and investigating crashes (where I took my own photos, starting my love of this field), I am not surprised that some of you are "harassed" by police. I can't count the number of cars I stopped for a traffic violation intending to write a warning, only to have the driver greet me with "What the **** do you want?" Guess what!! Every one of those drivers wound up with a ticket!! YOUR attitude goes a LONG way toward how the encounter will end. If some smart aleck handed me a card and gave me the name of his lawyer, we would have a much longer and much more unpleasant encounter than the guy who remained cheerful, positive, and simply told me what he (or she) was doing. Remember, law enforcement officers are supposed to check out anything that "doesn't look right". Don't automatically assume they are "picking on photographers. Oh, and keep the "Rights" card in your wallet, not in your hand! And, I know (and knew) what the rights of photographers were and are. My big problem was with the media, including one helicopter pilot jerk who was actually moving evidence around at the scene of a fatal crash which killed a police officer "to make a better shot". Things deteriorated rapidly for him when he told me to "Get out of my way, son. Don't you know who I am?" Do you know how hard it is to find a tow truck to remove a helicopter after the pilot has been arrested?

now it's getting interesting;
What if a mall security guard says to stop taking photos?

This comes down to photographing and trespassing being two different things. If a private security guard asks you to stop taking photos, you do not have to comply; you can still take photos. But if they ask you leave, then you have to leave, as your permission to enter has been revoked and you are now trespassing. However, you can take photos while walking out, and you can still publish those pictures. For more, see trespassing.
http://www.photosecrets.com/photography-law-permission-can-i-take-this-photo