Frogger reminds me the most because of the Dentist - I hate going to the dentist (and all the offices I went to had a arcade with Frogger lol)

So Donkey Kong gets my vote.

Galaga for me.

I have a soft spot for Frogger, but yeah its Donkey Kong.

Are we supposed to be voting as though we're casting this vote in 1981, or are we casting our vote in 2023?

I think if I were voting in 1981, I have to go with Ms. Pac-Man. That game was a mega hit, and a good evolution on a prior mega hit. It's significance was much greater than the other games in that year.

But, as 42 years have passed since then, I can recognize that other games had a more significant legacy. I'd say donkey Kong is probably the winner, because of the Donkey Kong and Mario characters that came out of it. Others have already done a good job of mentioning the influence that many of those other titles had on future games, and still have today. Ms Pac-Man did not, I think, do as much to influence gaming down the road.

You can use whatever criteria you think are appropriate.

Galaga was the most fun

Voted for the game I have played the most, which is Donkey Kong. Though admittedly, I played Donkey Kong Jr more when I was a kid.

Also, you should linked to your other Goty threads in your OP to chronicle the winners. 

I vote for Galaga as that was pure magic to me playing it on arcade machines. So smooth, so awesome to control. It inspired me to make my second full game (after pac-man) shooting waves of enemies and dodging asteroids. This one I had multi tasking working with everything animating on time. I wrote it in BASIC on the MSX which isn't fast, more enemies, more slow down. My solution was to let everything make bigger steps, basically my first attempt to code things based on time instead of let it run as fast as it can. It only ran at a few fps though, nothing like the sweet smoothness of Galaga.

Donkey Kong was the game that put Nintendo on the map. Without Donkey Kong, there would be no Super Mario Bros. and without Super Mario Bros. the 1985 test release of the NES in North America would've failed, and if the test release of the NES in North America failed, the big N's would've been a Japan-only market more or less. The Switch would not be the best-selling console of today. The PlayStation line of consoles probably wouldn't exist either because it was a byproduct of Sony's relationship with Nintendo. What kind of gaming landscape would we have today if not for those developments? It all comes back to Donkey Kong. Donkey Kong wins for that reason.

To commit a major gaming heresy though, I actually hated the original Donkey Kong, incidentally. I found it too difficult to successfully jump over barrels, and dying after I successfully reached the platform I was aiming for simply because I'd leapt from a centimeter too high frustrated me. I'd already played Super Mario Bros. first before discovering Donkey Kong and yeah Donkey Kong in comparison felt like a pretty big step backward from that in every way. So my choosing Donkey Kong here is definitely a matter of objectivity concerning its cultural impact, NOT my personal bias.

Had I to pick a game from 1981 that I personally liked best, honestly that would be Ms. Pac-Man. It's rare that I'd gravitate toward an arcade game over the more complex and interesting home computer games of the era like Ultima I, but Ms. Pac-Man is just absolute arcade perfection in every way I can think of. I still play it when I visit arcades today! It's faster-paced, more varied, and more animated than its predecessor and, together with the more clever intermissions, these simple alterations really do make the difference for me, I have to admit.

Hm...

Most influential - Ultima.

My most played, back in those days, from that year - Scramble (surprised not to see it in poll, since it was very successful hit and first side-forced-scrolling shooter).

Best - probably Galaga. It was fun then it is fun today.