My most memorable experience was at Yankee Stadium and involved Frank Robinson. I'll paste this from the Frank Robinson card entry on my 1959 Topps blog:
In 1969 I went with a buddy, also a Oriole fan, to see the O's play at Yankee Stadium on a mid-week afternoon. We'd decided that we'd make a couple of banners to support our club. We set to work dividing an old bed sheet and, with orange paint and a marker, we each created a work of art. His was the number '5' for Brooks Robinson. Mine was a '20' in orange with 'RF' added on.
We missed the Orioles' batting practice session but we hung out near the third base dugout in hopes the players would see our signs when they warmed up. Then a batboy approached me and asked if I would like him to take my banner to Frank in the clubhouse and show it to him. I said 'Sure' and handed it to him not knowing if I'd see it again. Moments later here comes my banner up the dugout steps being carried by Frank Robinson himself. He asked whose it was and brought it over to me and thanked me for bringing it. He asked for my pen and signed it right in the middle on the '0'. 42 years later I still have it. It's discolored and been stained a bit along the way, the orange color had darkened to a pinkish red and the autograph has faded some. But that banner still means more to me than any piece of memorabilia I own.
Now for the other end of the spectrum. This is from a comment I made once on Kevin's Orioles Card 'O' the Day blog:
Here is where I relate my most embarrassing moment in a big league park. Took my then girlfriend, now wife, up to Arlington to see the O's play the Rangers in '76. Tippy hadn't been with us long and I knew little about him. He was standing on the sidelines near the dugout and when he came over I had my wife ask him some dumb question about coming to the O's in Spanish. He looked at me and said 'I hope I do well for the city' in perfect English. I had no idea he was from Colorado. I looked like an idiot but he laughed and signed my scorecard.I don't have the scorecard handy. Since it wasn't an Orioles home game program there's a good chance it got shuffled out the door at some point. But I still have the memory of feeling like an idiot. Sadly, it wasn't the first or last time for that. Here's a Tippy Martinez 8x10 instead.