When I was in kindergarten (1988?) my dad proponed I walk myself to school and class. That was fine because it was only a couple of blocks away. He always had to pick me though, as I believe it was a requirement from the school.
Oh that dad, always willing to skirt those darn democrat rules that impede his work day 
I walked to kindergarten, with my 1-year older brother, but it was only two blocks.
On the other hand they did have a crossing guard for the 4-lane street with a stop light, so I was doubly covered.
I walked by myself to school (about 1/2 mile) when I was 5 1/2. When I was 8 I was escorting my 5 year old sister to kindergarten. The world was not necessarily a kinder gentler place back in the 70’s either–there was a weirdo in the neighborhood who liked to expose himself to kids. The school’s way of dealing with this was to send out a memo warning kids to walk in groups on their way to and from school.
I’ve never lived close enough to walk to school. At the moment, I walk half a mile to the station alone, get the train alone, and walk a mile and a half from the station to school alone. Busy roads all over the place. I’ve been doing this since I was twelve.
Man- my mom and I had an argument about this very question 2 weeks ago. We just recently let our 7 yo son walk the .75 mile home from school. Now he walks to school as well. He leaves while my husband is getting his younger brother ready for the special ed bus to get him. We live in a middle class, young neighborhood and usually there is another kid out walking as well, There is a cross guard at the busy street to get to the school, but I just found out last week that our son is jay running (!) across the street from my brother, who caught him that morning.
My mom had the audacity to say she NEVER let us walk to or from school until the 4th grade. Hah! I wish. Even my dad had to correct her, she was so off base. i walked home from second grade in 1979.