Big-time tennis appeals to all sorts of people for reasons as varied as the crowds that fill tennis stadiums in New York (rowdy), Paris (coolly critical) or Wimbledon (politely appreciative). Some people enjoy the simplicity of the sport. Some enjoy the human, immediately graspable physical scale of the court itself, while others — accomplished amateur players, for example, who know how hard it is to stay mentally tough and physically strong during a long match — stand in awe of how jaw-droppingly good the professionals really are.

Then there are those fans who thrill at the prospect of a singles final at center court in a major tournament — the tennis equivalent of a heavyweight title bout, but without all the split lips, swollen eyes, bloody noses and controversial, brawl-inducing decisions that boxing is heir to. The idea, after all, of two physically formidable combatants facing one another in an arena — surrounded by the immediate presence of several thousand riveted, passionate, vocal fans — has something almost primal about it: there will be a battle; the contestants are on their own; and at the end, there’s only one winner.

And, of course, one loser. Tennis is after all, a pitiless sport.

But pitiless or not, it’s also a sport that, every once in a while, is able to get people who ordinarily don’t pay any attention at all to the ATP or the WTA quite frantically worked up about tournament seeds, court conditions, ball boys and ball girls, line judges’ calls and Williams sisters’ outfits and, as the quarters and the semis and finals approach, about the matches and the players themselves. The Wimbledon Championships at the All England Club every summer is just such an event.

Sure, all the Slams have their strong points. The U.S. Open ripples with Gotham-sized attitude. The French Open has those cool-looking, bright orange clay courts. For fans, the Australian Open — held 10,000 miles away from the other three majors and played in what, for much of the world, is the dead of winter — feels like a holiday.

But then there’s the one. Ask one hundred players which major they’d want to win, if they could only win one in their entire career, and ninety-nine would say, “Wimbledon.” The grass is greener, the tennis whites are whiter and the history of the tournament itself is far, far more storied and memorable than that of the other three Slams combined.

Here, in the midst of the 2012 Wimbledon championships, LIFE.com offers a selection of photographs celebrating the sport: kids, adults, amateurs, professionals, men and women, all enjoying the singular pleasure of smacking the fur out of a yellow ball.