X-Wing (because I was, and still am, a Star Wars nerd)
Gauntlet (because I was, and still am, a D&D nerd)
Galaga
Gyruss (sort of a Galaga clone, only it was laid out in a circle)
Cyberball (futuristic football, played with robots and a ball that explodes if you don’t score in time)
I always opted for a challenge:
“Royal Rumble” mode, using “Million Dollar Man” Ted DiBiase.
The challenge was that he was one of the few characters who didn’t have a move to throw an opponent out of the ring (no body slam, back drop out of the ring, etc), so you had to actually beat your opponents and pin them to win.
There was an arcade in a neighboring community that had that cabinet for a while. I don’t think I ever played it.
Ground Kontrol in Portland had one when I went in January. It’s the only time I’ve seen one and had the opportunity to play it. I found the pinball part much more entertaining than the video game part, but I couldn’t figure out what makes the play transition from one to the other.
That reminds that Pizza Hut had sit-down tabletop video games. I think Centipede was one.
There’s a NY-style pizzeria here in Olympia that has a Centipede cocktail table, along with a few other vintage games and pinballs. I never remember to have quarters on hand when I go there, though.
Years ago, I was living in Toronto, and the corner pub had a cocktail table game. For the most part, it had video games (I particularly remember Galaga, which a friend got quite good at), but it once was swapped out for a cocktail table pinball.
Fascinating thing. The cabinet was octagonal, and while certainly not a regulation-size pinball, it had everything a regulation-size machine did. There were targets to drop, sequences to complete, bonus points to collect, and so on. It was fun to play, and I played a lot.
Then, the pub went back to a video game machine; and so, I went back to the TV behind the bar.
Back during the 1983 arcade bust, I bought an Asteroids, a Battlezone, and a Gravitar for around $400 and had those bad boys in my home for years.
My favorite game was Robotron: 2084 which I was very good at - like 6 hours on a quarter good, like I rolled-over my extra men good (255+1 flaw on 8-bit machines). Have a cabinet-sized mame emulator with Robotron (and Defender and Stargate and Joust and Tapper and Sinistar (possibly the hardest game I’ve ever tried to master) and Rampage) on it.
Galaga was fun, and so was its predecessor, Galaxian. Galaga had that bug where you could get the enemies to stop shooting, which made the game laughably easy.
I also thought Food Fight enjoyable, but was more difficult than Robotron given that you had to press a button to shoot, and your aim was controlled by the same joystick which controlled your movements.
One which I put a lot of quarters in, but was a complete pain (literally) to play, was the Football game with that big-assed trackball. Another sports-favorite of mine was Track and Field which I used the pen-between-my-fingers trick to gain record times.
… and, no, I was never adverse to cheating at the quarter-eaters. You programmed this thing and if you screwed it up - ala the patterns in Pac-Man - I was going to take advantage of it. After all, a quarter in 1979 is the equivalent of a $1 today, so not going to sweat cheating.
Glad to see Qix get mentioned, that was some creative game design, top-notch work.
Eight-Ball Deluxe was my go-to pinball game, but I also loved the short-lived (because it always was broken) Hyperball by Williams:
Centipede was also enjoyable, especially after you had built your wall, allowing you to funnel the centipede (and heads) down a single path.
Konami released a lot of shit, but they hit the target with side-scrollers Scramble and its ‘sequel’, Gradius. I loved THE FUCK out of Gradius.
Tempest was probably the coolest game of the 1980s, perfect controls, it looked fantastic, both luck and skill were needed, and it got insanely difficult as you proceeded through the levels. Great, great stuff.
By 1987 or so, I had ‘grown’ out of the arcade scene, so never really got into the fighting games. Probably the last game I played to master was the Dragon’s Lair follow-up, Space Ace, which… in retrospect… probably wasn’t all that good.
Can I just say FUCK THIS DAMN SITE AND ITS INABILITY TO EMBED YOUTUBE AND FLICKR LINKS!?!? Because that’s some prime, grade-A, BULLSHIT right there!
I don’t know about Flickr links, but the Youtube thing is a known Discourse bug and has been discussed numerous times. There’s a whole About This Site thread about it that contains the easy workaround, but I will post it here (again):
When creating a post that contains a Youtube link, first close the preview pane in the edit window. Insert the link on a separate line like you’re used to. If you have to edit your post later, insert “&1” (without the quotation marks) after the youtube link, and if you edit again, increment the number after the “&”. That’s all.
Ok, got it, thank you!
My MAME cabinet:
Do you recall how to do that?
An acquaintance of mine in college had a side business where he sold and installed chips (or was able to reprogram something) that made the Pac-Man pattern not work. Arcades or bars would buy them so people couldn’t squat on a machine forever for one quarter.
In wave 1 or two (both work), keep one of the bugs alive (I always selected one of the ones which was to the right-most part of the formation). Let that bug scroll and shoot for about 10 minutes, then, once it passes three times without shooting, kill it.
No other bugs will shoot after this.
I assume this works because of the 8-bit limitations of handling numbers greater than 255 (seen in Pac-Man ending at wave 255, also losing my Robotron extra men at 256), but I could be wrong.
You should be able to display flickr images if you use their share option and then copy the share link and paste in your post.
I love this video - so much nostalgia in it:
That cabinet is so cool! Color me jealous. Looks like some Rock Band or Guitar Hero controllers next to it, too. I want to have a playdate with you.
Later versions of Galaga fixed this glitch.
255 is also what causes Donkey Kong to end where it does, by causing the calculation as to how much time you have to finish the level be so low that it is impossible.
As for the original question, if I had to choose one arcade game as my “favorite,” I would go with the original Crazy Climber (not to be confused with the Donkey Kong clone “Crazy Kong”).
I enjoyed the 8-bit era musical rendition of “Mad World” by Tears for Fears.
Quartet (1986) - Easy to learn, impossible to master. Lots of colorful enemies and kept me on my toes every second.
Contra (1987) - My first platform shooter. Endlessly compelling. I never figured out which was the best weapon (it was the laser, BTW).
Shinobi (1987) - A more polished, more forgiving, smoother, prettier-looking Rolling Thunder. Jo Mushapi was one of the underrated greats.
Golden Axe (1988) - Quartet with edged weapons. The fourth level was a doozy.
Final Fight (1989) - My first token-gobbler. Enemies were borderline crazy but it was still highly satisfying to take them out.
Fatal Fury (1991) - While simplistic compared to SNK’s later fighting games, it was always a lot of fun figuring out what worked and what didn’t against each opponent. Ending was suitably haunting.
Spider-Man The Videogame (1991) - Beat-'em-up that really rewarded smart gameplay and proper timing. Enjoyed playing all four characters.
Sharpshooter (1998) - Charming low-difficulty shooter. I could routinely get all the way through on one credit.
Wangan Midnight Maximum Tune 3 (2007) - To this day I still consider this Namco’s best racing game ever. A rich story mode that’s not too difficult but can punish you if you get sloppy, the always-intense time attacks, and a lavish 10 Opponent Outrun which will test players of all skill levels.
Beatmania IIDX series - I cannot name anything else in my life which vexed me so utterly and yet always made me come back for more. These were hard, hard, HAAAAAAARDDD music games, and also pretty expensive everywhere they were. They drove me nuts and to tears on several occasions. It didn’t matter. The music was just so breathtaking, the videos so gorgeous, I couldn’t turn away. Pop 'n Music didn’t have the kind of iron grip on me that this did. Occasionally I look back on this time and honestly wonder what the hell happened.
I guess you had to be there. 
My favorites were:
Frogger - (I could consistently get the high score on the machine at our local supermarket, which made me feel a little bit special)
Star Rider - Very obscure, one of the first laserdisc games. We had it at my college arcade in the mid-80s, and I spent way too many quarters on it.
Tempest and Major Havoc - Vector graphics games from the same company. I liked them both, but preferred Major Havoc.
MotoRace 2000 - Another obscure one at our college arcade, where you rode a motorcycle at the bottom of the screen through the desert while the screen scrolled down past you and you had to avoid obstacles.
Star Wars - I don’t know if that was the actual name, but it was another vector graphics game where you did Luke’s run through the Death Star trench. It was a sit-in game, so it really felt like you were flying an X-Wing (as much as that was possible in the mid-80s.)
Space Ace - Another laserdisc game from the people who made Dragon’s Lair. It was frustrating as heck, but very satisfying when I finally managed to beat it.
Centipede - Almost forgot about this one, but it was one of my first favorites!
Every time I hear about Contra, it reminds me of this song (band was friends of friends back in the late '90s)
UP UP DOWN DOWN LEFT RIGHT LEFT RIGHT B A SELECT START! 