Dang, you GAFers have good taste.
This is a long list of games for me. I guess I'll start off with Magical Drop 3.
A good friend introduced me to the game on his Neo Geo MVS cab. I take the 2p spot, our Versus match begins, and within 10 seconds I've lost the first match. The second match didn't last any longer.
I hadn't been trounced that hard in any game since Street Fighter II in the 90s. I was hooked.
At that point of my life, I enjoyed a few other Vs Puzzle games and competitive arcade games in general, but Magical Drop 3 completely floored me by its simplicity + speed. It is a cruel, cruel game where a gap in skill between the players becomes immediately apparent. Similar to Tetris Attack / Panel de Pon, Magical Drop 3 allows you to add more bubbles mid-combo during a brief window of time. You can also manually add bubbles to yourself, so the good players will often overstack their own playing field and then clear it for a huge offensive attack.
If you look at the column between players, there's also a line tally. The first player to clear 300 lines automatically wins, in the event that a player isn't killed beforehand. Kills are far more common, but if you actually beat someone (or get beaten) by line count, you're likely playing against someone near your own skill level.
(an example of some high chains; timestamped at 8:55)
EDIT: as an aside, I should say this game jumpstarted my fondness of Vs Puzzle games. After MD3, I fell in love with others like Landmaker, Money Puzzle Exchanger, and Cleopatra's Fortune.