This is a neat question AK. First, I definitely remember the Brooks Robinson series noted above against the Reds. They called him the human vacuum sweeper. The year after, one of my boyhood favorites - Roberto Clemente put on a show against those same Orioles.
My most memorable game was a perfect game and I watched it on TV but there was a story to it. The fact I even watched it was the story. All during the 60's, 70's, and 80's the Indians were probably the worst run franchise in all of sports. It seemed when they had hitting they did not have the pitching and visa versa. They were perennial losers and hence often only drew about 5,000 fans per game on most nights. Looking back, it is amazing they drew that many.
Anyhoo... it was a Friday night in the spring of 1980, I was 20 years old, and all my friends wanted to go out as we always did on Friday nights. Not for me this night. I said, "I want to stay home and watch the Indians." They said, "The Indians, are you nuts!!"
I said, I want to watch Len Barker pitch tonight because he really has impressed me thus far. He has got an outstanding fastball and a really good breaking ball. That didn't seem to convince them
Well... after about seven innings, Len Barker was mowing them down with one of the best curve balls I have ever seen. Knee-buckling curve balls. All of a sudden, people started showing up at my house. They said "Do you realize what is happening down at the Stadium?" No duh! Being supersticious about baseball, I said "If anyone of you knuckleheads mouths the words about what is going on down there, I will never speak to you again and you will have to fight me out on my front lawn after the game"
The final innings of that game were some of the most exciting/breath-taking I have ever experienced. Len Barker ended up throwing the 14th perfect game in major league history that night. He is still a legend in Cleveland to this day and makes his home here.
Here is the funny thing. Ask anyone from Cleveland who was around that night and they will tell you they were at that game. The announced attendance was less than 5,000 and from the looks of it on TV, there were probably less than 2,000 at the game. Now you know the rest of the story....