Americans typically enjoy their personal space. In rare or normalized occasions, such as taking a crowded bus to a concert or even riding the Subway to work, people in the U.S have all experienced an invasion of their personal space. Usually, however, this invasion is only acceptable when you put yourself in situations where you know it is going to be crowded. Any other invasion of personal space is unexpected and unwelcome.
It is interesting to see how American society innately seems to keep a comfortable distance from strangers. For example, when you go to sit on a bench with someone else on it, your first inclination would most likely be to sit a decent distance away from that stranger.
Similarly, if you walk into class on the first day of school and there is one person on the far right of the room, you might choose to sit to the right of the room, unless that person is your friend. In America, physical interactions are usually kept polite and at a distance.
This societal norm, however, is very different in other parts of the world, such as Europe. For example, Italy embraces closeness. They tend to be more touchy-feely in general. For example, when two Americans meet for the first time, it is typical to shake hands. In Italy, it is typical to hug the person you just met or even kiss them on the cheek in a friendly greeting.
Another thing that can be noted is a public display of affection. In America, it is typical to see couples holding hands down the street whereas, in Italy and a bunch of other European countries, it is common to see couples intimately kissing out in public.