As I see it, its between a Triple Play, An Inside The Park Home Run and Stealing Home.
IMHO its the Inside The Park Home Run simply because the play lasts longer. You want excitement? How about a walk off inside the park grand slam home run. Don’t think this has even happened.
It’s down to Inside the Park HR or Triple Play. Stealing home is exciting, but over quickly, and it’s pretty much the same getting to home from 3rd on the Inside HR. Sometimes each of those is just a comedy of errors. So which is more exciting? One’s a winner on offense, the other on defense. I’d just leave them as the most exciting in each of those categories.
If sheer rarity is a criterion, in addition to actual excitement, i’d nominate the unassisted triple play. Only happened 15 times in the modern era of baseball.
For more common plays, i really like the bases-clearing triple. A triple by itself is relatively unusual, but when the bases are loaded you get all fours runners in motion. It’s great to watch.
Maybe not as exciting but vastly amusing is the Little League Home Run. An ordinary fly ball or line drive turns into a series of errors that allow the batter to score.
How about the unassisted triple play? I’ve been to a game with one of these. I’m not sure it’s that exciting–it happens so fast you don’t have time to react (and I, in fact, was looking away when it happened), but it’s rarer than a perfect game.
Detroit Tigers Hall-of-Famer Sam Crawford told of a play that he and Ty Cobb would sometimes pull:
Crawford followed Cobb in the batting order, so when he came to bat, Cobb would sometimes be on third base. If Crawford then received a base on balls, he would trot down to first, and then, without stopping, break into a run towards second.
The team in the field had to then quickly choose between 1) throwing to second to get Crawford out (which increased the (already high) likelihood that Cobb would try to steal home); and 2) letting Crawford reach second, while preventing Cobb from stealing home.
Crawford said it was a very exciting play. Sometimes they would get him out, sometimes they would get Cobb out, but most often he would wind up on second from a base on balls.
When I was a softball umpire, runners and first and third used to be an automatic steal. Then one day I was shocked to see the catcher come up firing on such a steal. The runner on third came home for the easy run. Then the shortstop cut off the throw at the just shy of the pitcher’s rubber and fired home for the easy out. The poor guy looked like a deer in the headlights.
I was at the Blue Jays - Orioles game a couple weeks ago when something similar happened. A ball that didn’t leave the infield (except for throwing errors; like your link, it was hit back to the pitcher) ended up having the batter (Darwin Barney) come all the way around, scoring three (including himself.) It was this play. (5:45 if the timestamp link doesn’t work properly.) Weirdest play to get the runner around four bases I’ve ever seen. Error on the play to first, and then a casual throwback to the pitcher somehow ends up in the dugout, and all runners come around.
I was in left field trying to figure out what the hell just happened. At least this time I was actually watching the field of play.
ETA: Now that I think of it, I’ve had pretty good luck at games at visitor’s parks. I’ve only been to three fields outside Chicago, and one day (at Fenway) it was the unassisted triple play, another day (this year) was when all the home teams won on a full slated day (I was at Kaufmann Stadium in KC), and then this game at Camden with those freak show errors.