When I was 5 years old, I had a huge crush on Michael Ansara, who starred in Broken Arrow. That was back in 1958. My dad was stationed in Wichita, KS for 12 weeks with the Air Force, and my mom took me to a rodeo, where I got to meet my crush and shake his hand. I doubt he was very impressed, as my mom was carrying me.
I've also met Peter, Paul and Mary and talked to them backstage.
When I was a teenager, my girlfriend and I went to the Ohio State Fair to see Ed Ames, who was in the singing group the Ames Brothers, and also played the role of Mingo, the Oxford-educated Indian friend of Dan'l Boone (another crush of mine...I'm seeing a pattern here with the roles they played) sing in concert. We stood on folding chairs right in front of the runway, and touched his shoe as he walked past! Wow! We stayed for both concerts. That man could sing anything...and he still sings, even at age 88 or so.
Also as a teenager, my dad, who worked at Executive Jet as a dispatcher, tipped us off that Johnny Carson was flying with them. My mom and I parked by the building, and when he came out, she yelled, "Hi Johnny!" He looked a little scared.
Oh, and once in the 1980's, I was working for an accounting firm, and took a phone call from John Glenn's wife, Annie.