Perhaps you, like I hitchhiked when you were young. It was a common occurrence in the 60s and even into the early 70s. Even attractive young women felt safe hitchhiking.

So what happened, and when?

I believe that people began to feel less safe hitchhiking partly because of such highly publicized cases as that of the 'Zodiac Killer'.

Also, as the counterculture movement was winding down hitchhiking didn't so much display a nonconformist attitude as a lack of responsibility and failure to be successful in living a good life.

Another factor is the increase in car ownership around this time and the proliferation of Interstate highways where higher speeds made stopping more dangerous.

I think another important factor is a general erosion of trust across society at large. 

Remember when people felt comfortable leaving their car and home unlocked?