"Best" in what way?
Anyway, here are my three:
1. Daly What's My Line? (the one where he is the final mystery guest...and I think I know the story of "the one mystery guest who arrived with a minute to spare"; I remember reading a story about a celebrity who was sitting down to watch TV, heard the announcer say, "Stay tuned for WML?", and suddenly remember that he was the mystery guest that night)
2. NBC Chain Reaction
3. NBC Hollywood Squares - they brought a contestant back and credited her with $1800 so she only needed to win one game to get the 5-match "jackpot," but she then lost her next two games
Honorable Mentions:
The Better Sex - IIRC, rather than start a game they knew wouldn't end in time, they just had Bill Anderson break out his guitar for a song.
The Gong Show