This one is hard for me because I literally spent a good chunk of my pre-teen/teen years in an arcade every day after school and all day saturday because my cousin managed the one at the end of my block. But standouts due to just how much I played them BITD compared to the many others. In no order:
Joust - perhaps the first game I became totally hooked on. Joust was my go-to game at every arcade I would visit. I got pretty good at it too.
Dragon's Lair - At one time with the game set on the hardest setting I beat the record listed by Twin Galaxies and submitted my score. I found out nearly 20 years later when meeting Walter Day that many records from the time period I submitted it in were lost in a move! I once beat this game set on 5 lives playing "blind" as the monitor was broken. 3 people witnessed it and were in awe that I could play just by the sounds. Luck played a good part in picking the right first move for the boards that were mirrored but i was so familiar with that particular machine I knew which version was favored by it as I used to play it every day.
Tempest - Fell in love with it much like I did with Joust .
Track and Field - I still have my "high score of the week" trophy I won at the local arcade when it first came out. I never used any comb or any gimmicks when I played. Our local arcade put those button guards on their machine a couple weeks after they first put it out on the floor.
Xevious - I had a friend named Ken who used to hang out at the arcade who was a few years older than me and we used to play 2 player all the time on this one. We were both good at it and we pushed ourselves to get better by trying to top each other's scores. This was the first game I ever owned in my home and I sometimes regret selling it.
Honorable mentions:
Argus/protector/guardian: Gottleib/Mylstar used to test games at our arcade and they put this one there at least two different times under different names. I loved that game and recently discovered it is playable in MAME. I was bummed when that game never got released and when they took it out of the arcade. Having not played it in over 20 years I was so happy when it still held up for me. It was the catalyst behind having a friend put together a MAME cabinet for me that I will be receiving shortly
Gyruss - I loved this more than galaga and the music remains among the best in video game history for me
Punch Out - When I was a kid I put up a 1,999,990 game (it flips at 1M) and could have easily beat the 8M world record at the time had my cousin not physically picked me up and pulled me away from the game. Customers waiting to play for over an hour complained about me "hogging it" and since they were paying for their games and I wasn't, he made me stop.