Depending on the era:
Being the best team in NBA for sometime it varied between:
Detroit Pistons (Hacking MJ; The Detroit Bad Boys Champions 1989/1990, Bulls 1991-93)
New York Knicks (Eastern Conference Championship Rivalry Ewing Vs MJ)
Indiana Pacers (Jordan Vs Miller; the infamous fight)
Utah Jazz (Stockton and Malone Vs MJ and Pippen; who is the best dynamic duo of baskeball)
In my opinion, I'd say Detroit due to the fact that their was hatred their, a violent rivalry and you will notice the NBA still do talk up Pistons Vs Bulls matches as something big as traditionally these teams have been solid in the East but not too recently have Chicago.
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Lakers. They've faced each other ten times already and this year it makes it 11 meetings at the Finals.
The New York Yankees and The Boston Red Sox.
Before they moved to Washington, the Montreal Expos were also a rival of the Blue Jays.
The rays are another division rival