Over the course of a 23-season career filled with milestones that other ballplayers only dream about, Hank Aaron retired as a first-ballot Hall of Famer and, most famously, as the all-time major-league home run king. Today, for most fans, he’s still the all-time major-league home run king — Barry Bonds’ 762 career round-trippers notwithstanding. So many other numbers that he put up over the course of his career, meanwhile, cement his reputation as one of the very greatest ballplayers who ever lived.

To cite just a few of his eye-popping stats: Aaron was a 25-time All Star (from 1959-1962, he played in both of the All-Star games held each summer back then) and a .305 lifetime hitter. He slugged 755 home runs, of course; had more than 3,700 hits, including a major-league record 1,477 for extra bases; drove in 2,297 runs (another major-league record); won a World Series ring; won a couple of batting titles; and, perhaps most incredibly, he still holds the major-league record of 17 consecutive seasons with 150 or more hits.

Take a moment to digest that: 17 years in a row with 150 or more hits. Anyone who knows anything about baseball knows that it’s hard to get 150 hits in one season. To hit 150 or more, year after year for almost two decades, while routinely launching 30 or more home runs every year, speaks to a talent, a competitiveness and a consistency that borders on the superhuman.

Henry Aaron spoke with LIFE.com about some of the players — teammates as well as rivals — who made his playing days so satisfying, and so downright fun, for so many years. Now 79 years old (b. Feb 5, 1934), he is as gracious as he is insightful in his praise of his friends and foes. On top of everything else, he is a man of quiet, undeniable dignity.

Happy birthday, Mr. Aaron. And thanks for the memories.

— Ben Cosgrove is the Editor of LIFE.com

NOTE: This gallery appeared, in slightly different form, on a previous incarnation of LIFE.com.