For instance, there was Zimmer's friendship with Jackie Robinson. He and Jackie had been teammates with the Dodgers, but they had drifted apart through the years.
And then one day, Zimmer answered his phone and heard Robinson's voice. He was coming to Florida, and he wanted to know if they could play golf.
Robinson appreciated the way Zimmer treated him when they were teammates. Like a lot of people, he recognized that Don Zimmer had a huge, loving heart.
For his part, Zimmer had watched Robinson. He'd seen not just the amazing athleticism, but the courage and dignity that was almost beyond comprehension.
Later in life, Zimmer was so overwhelmed by their friendship that he had trouble talking about it.
"Look, I don't get it," Zimmer would say, choking back tears. "What would a great man like that see in someone like me?"
That's the easy one. People loved Don Zimmer. They loved his laugh. They loved his loyalty. They loved the sheer joy he exuded when he was at the ballpark.
Upon hearing of Zimmer's death at 83 on Wednesday, there were hundreds of people who felt they lost a best friend. That's because Zimmer had the ability to make someone feel that the five minutes he spent with them was the best five minutes of his day.
Joe Torre loved Zimmer like a brother. Jim Leyland spoke to him virtually every day. When Zimmer worked for the Rays in the final years of his life, he lit up every room.
Zimmer would smile. He would tease. The Rays gave it back to Zimmer, too. Once a club employee handed him a slip of paper with a telephone number.
"Sports Illustrated is doing a story on Ty Cobb and wants to talk to some people who knew him," the man said, as the story goes.
Zimmer looked at the number, looked at the prankster and sputtered.
"How old do you think I am?" he hollered.
At that, the club employee broke down in laughter, and Zimmer knew he'd been had again.
Zimmer gave it back, too. He walked in one day and screamed, "Who has been giving my telephone number to these writers?"
Uh, I have, one guy stammered.
"Honest, Zim, I didn't think you'd mind," he added.
Zim stared at the transgressor for 10 seconds, then burst into laughter.
Zimmer's baseball knowledge was incredible. Once, when he saw a kid in a bunting drill, he walked over and interrupted.
"I know who taught you how to bunt," Zim said.
Zimmer mentioned the name of a longtime baseball guy.
"That's right," the kid said.
Later, someone asked how Zimmer knew that. He said certain people taught bunting a certain way. Zim recognized the technique instantly.
Zimmer saw baseball from every angle. He played parts of 12 seasons in the big leagues, mostly as a part-timer. He played another eight seasons in the Minors and one in Japan.
Zimmer had 500 plate appearances only once in his career. That was in 1961, when Ron Santo's big league debut prompted the Cubs to move him across the diamond to second.
There, in 1961, Zimmer had his finest season and made the National League All-Star Team. Mostly, though, he had to scuffle for a job throughout his career.
As Zimmer was moved around, up, down, here and there pursing jobs in baseball, he would almost always interrupt the story to nod at Soot, his wife of 62 years, and tell how she kept the house running, kept the children in line. They were married in 1951 at home plate at Dunn Field in Elmira, N.Y., where Zimmer played for the Pioneers at the time, and theirs was a marriage of love and laughter.
Once Zimmer's playing career ended, he made four managing stops over 13 years. He won 90 games four times, including 99 for the 1978 Red Sox, who are best remembered for Bucky Dent's home run in the 163rd game of the season.
Zimmer found out that Boston was a tough job. He seemed addicted to the misery of talk radio, but he also appreciated the opportunity to manage.
Zim loved Los Angeles the same as he'd loved Elmira. As long as they paid him to put on a uniform, as long as they paid him to do what he would have done for free, he was about the happiest man on earth.
Zimmer loved that big leaguers got treated to first-class travel and nice hotels. But some of his fondest memories were traveling by bus in the Minors and staying in fleabag hotels. He thought that was a pretty good life, too.
No man ever loved his job more than Don Zimmer loved his. Even late in life as he struggled with an assortment of health issues, he came to the park when he could.
He cackled when the Rays did a "Don Zimmer Night" in which they handed out Zim dolls. When they showed him a mock-up of the dolls, they worried that he would be unhappy.
"Hey," he roared, "I know what I look like."
In the later years of his life, Zimmer would enter a ballpark and soon be surrounded by players, coaches, cops, ushers, sportswriters, etc. They wanted to be in his presence. They wanted to hear him laugh and perhaps make him laugh.
On Wednesday, all those people, hundreds of them scattered across this great country, felt an emptiness that they'll never hear that laugh again, that they'll never share another meal or ask Zimmer about the ponies.
Maybe Zimmer was right that he was one of the real lucky people on earth. But the really lucky ones are those who got to know Zimmer, from Leyland and Torre, from Commissioner Bud Selig to hundreds of others who write columns and wait tables and all the rest. They are awed by the life Zimmer led, the friendships he forged. They'll also miss him dearly.