Things took a turn for the weird by the time I was in college; one summer I wanted to take the bus up to NYC to visit a friend, and my mom (who, remember, had no problem with me just taking off on my bike when I was 8) was absolutely terrified that I'd be killed. She gave me her cell phone for the trip and insisted that I call her any time I were to leave or arrive somewhere. (This was all before 9/11.)
I don't remember any sharp change in her attitude toward this at any point, so I can only assume it was a gradual thing.
I hope saner and calmer voices prevail in the future.
I don't know how accurate it is, but there's this idea that child abductions and various other dangers (falling in an old well) in the late '80s, early '90s made parents more wary of letting their kids roam.
I strongly recommend the episode of the same name on the You're Wrong About podcast.
Then I got into computers and didn't see the light for a few years.
One very noticeable recent-ish norm shift seems to be parents dropping off and picking up elementary and middle-school age kids at school. I don't know exactly when the trend started, but it seemed to hit critical mass after 9/11, and over the course of the following decade seemed to become the norm to the extent that suburban schools started remodeling their grounds and parking lots to accommodate a waiting line of parents in cars - something I've seen now in multiple states.
Sometimes freak events have an oversized effect on people. In the US people used to park their baby strollers outside stores while they went shopping. One day, I think in the mid 50s, on Long Island, I believe, a family’s sleeping toddler in a stroller/pram was abducted and scared everyone from leaving their kids unattended in a stroller.
There are definitely differences between cultures when it comes to this, in particular when it includes raising children. Being German I actually got a lot of confused looks when we had American friends over and they noticed that young kids over here just go grab their bike, drive off and play in the nearby forest all day. They seemed totally shocked that ten year olds just run off and play in nature.