Mulder and Scully on The X-Files. They became romantic at the end of the series, but I liked them better as friends.
Karen and Richard on Knots Landing
Mack and Greg on Knots Landing. They became enemies at times, but you could still tell there was a friendship.
Donna and Miss Ellie on Dallas
Donna and Bobby on Dallas
George Jefferson and Harry Bentley on The Jeffersons
Ralph and Ed on The Honeymooners
All of the Golden Girls
Lucy and Ethel on I Love Lucy- The gold standard for friendship.