I think no matter where you travel if you're seen to be a tourist some people will see you as a "target" for petty crime of opportunity like pickpocketing. But in some countries being an American could make you the target of a violent crime committed by a political/ideological extremist. When I was in Marseille, for example, several American students studying abroad were the target of an acid attack.

I suppose the thinking goes that if one American is a potential target for an opportunistic violent extremist than a place that's frequently host to groups of Americans is perhaps more likely to be a target for a coordinated attack.

It might or might not be true but for the most part it wasn't particularly difficult to avoid my fellow Americans while traveling anyway. We tend to take business trips abroad but not many weeks-long exploratory vacations. Plus, you can't really get much of a feel for the country you're in from a Hilton now can you?

Edit: To add that I don't want to be fear-mongering. I think a lot of my friends and family thought I was taking a "risk" by traveling to some of the countries I went to and for the most part I felt just as safe in the Middle East as I did in New Orleans. I don't think fear should stop anyone from traveling but I also think it's wise to be mindful of some of the unfortunate realities of the world in which we live.