There are tons of panhandlers in New York (where I live). It's easy to shrug them off because New York is so busy they if they don't think they'll get anything from you, they just move on to the next person. Generally when somebody asks me for something I just say "sorry" or "excuse me" and just keep briskly walking. I don't look at them or say anything more than that. If there is a traffic light or something stopping me I just act like I'm going a different way than I'm really going and then double back because they aren't really paying attention to me anyway.
However once I visited San Francisco and that didn't work at all because it isn't nearly as busy so it's hard for them to move on to the next guy. Two or three times some guy followed me for like a full minute yelling at me while I continued ignoring them until I turned a corner and they lost interest. If I was a smaller person it could have gotten violent. I'm wondering how people generally go about shrugging off beggars in other locations, specifically France, UK and northern Europe, but answers about anywhere are welcome. Is flat out ignoring people a big enough insult to get punched by someone from those countries (although I would guess that beggars are often not actually from those countries, but you get the idea)?
Edit: Fixed title; "handler" should be "panhandler"