Some games, like Pac-Man have some sort of end point, and a maximum possible score (3,333,360). Some games have no points at all (FPS, racing games). But which game has the highest ever score? Doesn’t matter if it’s an actual score, the number of XP your Cleric has, I’m just after the biggest number.
Probably the 32bit integer limit: 4,294,967,295.
So any game using a long integer to hold its score. I don’t know what game lets you reach this number the quickest though.
The game with the most inflated scoring that I’ve played is Giga Wing. My personal best is 6,966,556,175,110 but, of course, the serious fans of the game get many times higher than that. Of particular amusement is the way they color-code the score display - it effectively begins with the hundred-millions digit 
Pinball machines from about 1985 on are often the same way with their scores. Most of them might as well be incrementing in 100 million point steps.
I hear you. In college, we used to measure our manhood on RoGo at 10,000 points to the inch. Now you get 100 million points just for pulling the freaking plunger.
I once got the population of a city so high in Civ 3 that it wrapped around this value several times. It’s a bit amusing, because “legitimate” city populations are always a multiple of 1000, so they could have just kept a count of the thousands, hard-coded those last three zeroes, and had a limit a thousand times greater, but they didn’t. Then again, since it requires not-quite-cheating-but-definitely-an-exploit to get population up that high, it’s not too big a deal.
I’m not sure this would count for the OP, though, since the only measure of in-game significance is population points, not actual population, which is much lower (i.e., you’d say “I have a city of size 20”, not “I have a city of population 3 million”).
The important metric is probably “number of significan’t digits” - who cares if the score is in quadrillions if the lowest possible score (other than 0) is 100million?
(some old pinball games juats the trailing zeros painted on)
Lookslike Giga wing at least uses the 10s digit for at least 12 significant digits.
Brian
An old MMORPG called Asheron’s Call has an xp scale that goes to 98,081,682,817 to reach level 240, and it looks like it really goes up to at least level 275.
It almost doesn’t count though because the game became a contest of who could write the best macro to level their characters while they slept. There are tons of maxed out characters, but nobody really earned that score.
ETA: You also gain tons of free xp from other people in your guild