'Infamous' obviously means that these have to be negative emotion draws.
I was at the 1981 FA Cup Final but I actually feel three others are worthy of a mention ahead of it for infamy.
1 - City 3 Bournemouth 3 in 1989- 3-0 up at half time and, ultimately, a win would have taken us up on the day if Palace didn't win also, and they were losing 1-0 at half time. It ends up 3-3 courtesy of a 97th minute penalty and Palace were winning as we left the ground. They also conceded in injury time, though, and strangely, we were in exactly the same situation as we would have been had we hung on for the win and they also won, but it sure didn't feel like it. I remember seeing quite a few sat on the Kippax crying at the end.
2 - City 3 United 3 in 1990. We played better in this one than we did in the 5-1 and were dominant for a full 80 minutes. We should already have been well clear when Colin Hendry put us 3-1 up with ten minutes to go. We all partied. We'd knobbed them again. Reidy goes off. Brighters comes on, loses the ball with his first touch, and by the 83rd minute it was 3-3. Only a superb save from Tony Coton at the end stopped them from winning it. I felt devastated that night, because I had my victory speech prepared, written and spoken. At least I didn't know then it would be another 12 years before we'd beat them again.
3. City 2 Liverpool 2 in 1996. Needed to better the result of one of Southampton or Coventry, who I suppose we expected to win their home games, which would have deemed ours irrelevant. We effectively put the ball in for them twice when they actively seemed to be trying not to beat us. We got back to 2-2, then with us needing the win, Stevie Lomas took it to the corner flag in stoppage time.