There can't be very many Hall of Famers out there who aren't even the best players at their own position to be born on their birthday, but Cuyler is one (at least if the position is "outfield"); Cuyler would be 112 years old today, but one Ted Williams would be 92.
Hazen Shirley Cuyler was called "Kiki" -- not "key-key," as in your old sorority sister, but "kye-kye," as in, well, nothing else in the world -- because as a young man, he reportedly had a stutter, so that's how his last name would come out of his own mouth. All those nicknames and such back in the day were pretty great, generally speaking, but they could be awfully mean too.
Cuyler was inducted to the Hall of Fame in 1968, which is very close to the time when Frankie Frisch was attempting to get every player he ever appeared in a game with into the Hall (though what research I've been able to do suggests that Frisch didn't really take over on the Vet's Committee for a year or two after Cuyler's election). In a lot of ways, Cuyler looks a lot like one of those head-scratchers; he has the pretty .321 batting average, but never won a batting (or an on-base, or a slugging) title. He hit .321 at a time when the average hitter (in Cuyler's park) hit .291. Cuyler didn't lead the league in much else, either; a doubles title, a triples title, several stolen base titles (in years for which we don't have caught stealing totals), and two consecutive times leading the league in runs at the start of his career...and that's about it. Cuyler's career wasn't particularly long, and he wasn't especially dominant in anything.
But at the same time, Cuyler was no Chick Hafey or Freddie Lindstrom. His 8098 PA is very low for a Hall of Famer, but still a good four or five seasons' worth more than Hafey or Hack Wilson. While Cuyler was never dominant, he was very, very good for a fairly long time, and paired it with some very good defense, as well. All together, his WAR (49.6 by Baseball-Reference, 56.2 per FanGraphs) is considerably lower than the most recent questionable Hall of Fame outfielder, Andre Dawson (57.0, 62.3), but a bit better than 2009's horrible choice, Jim Rice (41.5, 56.1).
So, where am I going with this? I have no idea. There isn't really that much of a reason to put a guy like Cuyler in the Hall of Fame, but he also shouldn't be lumped in with your Hafeys, Wilsons and Jesse Haineses. He was a damn good player, even if he's only the second-best mostly-corner-outfielder to celebrate his birthday on August 30.