How do Italian men treat American women?

My family and I are going to Italy in a few months, and right after I told my friends about it they told me to be careful because men are really persistant and follow you around sometimes. I know that every man is different, and I do not want to generalize, however I'm a little concerned. I also know there would be worse places to visit! I don't expect to have any issues because I dress modestly and don't act slutty, but I want to enjoy my vacation. Has anyone who has been there ever had any issues with this?