I've met Ted Dibiase and Diamond Dallas Page and Jerry Rice but the most time I've spent with someone famous was with Jeff Brantley on Super Bowl Sunday 1990.
My uncle had built his former house in Old Vineyard in Clinton and my dad was going over there to help the uncle with a fence, and took me along. Got to play horse with Jeff next door at his neighbor's house for a couple hours and he was incredibly cool, destroyed us in horse (never play a professional athlete in anything not their main sport, they will still kill you), and wound up giving me some Giants magazine and signing a bunch of cards for me. Later on my stepmother did a plywood yard decoration for him of a Santa wearing a Giants hat winding up and throwing a pitch to a separate elf in catcher's gear, and I got to go over there again and get even more cards signed. I think I ended up with at least 15 signed Brantley cards I still have.
Postscript to this story, 35 years later: we changed churches last summer, and in December we were there and lo and behold Jeff Brantley and his family were there and did the advent candle one Sunday. This past Sunday, two days ago, we got in the sanctuary a little early, and I realized Jeff and his wife were sitting a couple rows in front of me, so I went and asked to make sure it was him, and got to sit down and tell him that story and thank him for being so cool to a 13-year-old Giants fan all those many years ago. I was truly the coolest thing that could have happened to me in 8th grade. Jeff is a great dude, couldn't be a nicer man.