My experience was in the state of Missouri. When I was hospitalized (in the year 2000), I spent a couple of weeks in the ICU.
-I was 17 years old, so as far as decision making, I was considered a minor and all decisions were made by my parents.
-When I was in the ICU, I was limited to two or sometimes three visitors, but one of those "visitors" was always one of my parents. There was a little waiting area outside the ICU. When there was a new visitor, one of the nurses would tell my parents, and they would come "meet" the visitor in that waiting area, then guide him/her back to my room. (Three visitors was usually one of my parents with a husband and wife. Also the nurses could crack down on the visitors anytime they felt the number was becoming a problem.)
-A fair number of those visitors did not come beyond the waiting area. This was not due to any kind of law or rules, but just squeamishness. I was attached to a bunch of tubes and machines, plus needles (IVs, etc.). Also, the ICU was very open, so if they came into the ICU they could not avoid seeing the other ICU patients (who also looked very... sick.)
-Flowers were not allowed in the ICU rooms, but still, plenty of people sent bouquets. The flowers would be placed on the nurses' desk, which was in the center of the ICU, so the nurses and all the patients/visitors could enjoy them.
-In terms of laws, there were no laws prohibiting non-family visitors. The closest relative/decision maker could choose to prohibit visitors in almost any way he/she wanted. I had plenty of non-family visitors (teachers, other students, family friends). My parents would meet the visitors in the waiting area (which, as I understand, was the most common way for families to deal with visitors).
If I think of anything else, I'll let you know.