There's always something to talk about when these two clubs play each other, and there always will be. On the field, there have been epic battles, crushing defeats, joyous victories, historic collapses and bench-clearing brawls.
Off the field, however, the players and personnel on the clubs respect each other. Believe it or not, there's also a lot of love shared between the competitors.
That affection became evident for Red Sox first-base coach Ron Johnson and his family last September.
Johnson's daughter, Bridget, lost her left leg -- and nearly her life -- on Aug. 1, 2010. She was 10 at the time. Bridget and her older sister, Cheyanne, were riding their horses near the family's 15-acre farm in Morrison, Tenn., when Bridget and her horse, Rhonda, were hit by a car.
Johnson was in Boston with the Red Sox and immediately made arrangements to get home and meet his family at Vanderbilt Children's Hospital in Nashville. In the 34 days she spent in the hospital, Bridget had more than a dozen surgeries before returning home on Sept. 4. She was missing her leg from the top of the knee down.
Johnson never left his daughter's side.
When the family arrived home, there were letters, packages and gifts from all over. As Johnson was going through them, a specific package caught his attention.
"Everything during that time was so foggy," Johnson said recently. "We got home after Bridget got out of the hospital and this package showed up from the Yankees. I was like, 'What the f---?'"
Johnson opened the package and saw it was from Yankees hitting coach Kevin Long.
Long and Johnson have been friends since "RJ" was Long's manager at Double-A Wichita (Kansas City Royals) in 1995. A season later, Long's playing career was over and he began coaching with Johnson's help.
Now both are coaching in the big leagues and they remain close.
When the Yankees hosted the Red Sox at Yankee Stadium in the weeks following the accident, Long noticed Johnson wasn't around, so he asked Red Sox staff assistant Rob Leary why. When Long heard what had happened to Bridget, he decided to help out.
Long held a team meeting with the Yankees and explained the situation. The players decided to pass the hat and collect money for the Johnson family.
"I went to the guys, we had a team meeting, we talked about it," Long told Yankees beat writer Dan Barbarisi of The Wall Street Journal. "Right away, our guys were very gracious, and gave whatever money we collected."
When Johnson opened the package, there was a letter from Long.
The note read: "I didn't forget what you did for me. I know you're going through some tough times, so I hope this helps."
The Red Sox players had already done the same thing for Johnson, and the Yankees' gift is said to be around the same amount the Red Sox raised.
"It was incredible," Johnson said. "I showed it to [my wife] Daphane and she started crying."
Johnson immediately called Long to thank him for the generous gift. During their phone conversation, Long told Johnson to spend it however needed.
"He was very grateful and very gracious, and said he couldn't thank me enough," Long said. "We're very good friends. Unfortunately, we don't get to see each other and our families don't get together as often as we'd like."
When the Yankees host the Red Sox on Friday night at Legends Field in Tampa, Johnson will get to thank Long and the Yankees players in person.
"I told Theo [Epstein], 'When we play the Yankees and you see me thanking some guys, don't think I'm going over there bulls-------,'" Johnson said.
While the organizations are on-field enemies, what the Yankees did shows the human element to the game.
"Yeah, it's a rivalry, but it makes everything so much clearer that there's baseball and then there's the human aspect," Johnson said. "I know there's stuff that happens on the field, but they're human beings, and it's real neat [what they did].
"As I've seen more than anybody, the support I've had from the Red Sox organization is unbelievable. This was just another piece -- a phenomenal deed. Amazing."
There's a chance that Bridget Johnson will throw out the ceremonial first pitch on April 8 when the Red Sox host the Yankees at Fenway Park.
"I can't speak for them -- I know Kevin Long is a good friend of RJ's and it sounds like he really went out of his way to make a special moment for Bridget," said Red Sox manager Terry Francona, "and I think that happens in the game more than people realize.
"When you're on the field, you want to beat people's brains out. But when things like this happen, it doesn't take away any of the competitiveness of the game but I think it's a wonderful gesture what they did. It's a very heartwarming story, and I think it happens more than people realize."
It's another great chapter to one of the greatest rivalries in sports.
Joe McDonald covers the Red Sox for ESPNBoston.com.