For me, I finally got to enjoy games like "Robotron" that I sucked so bad at I couldn't, at the time, justify spending a quarter on about a minute of game-play.
MAME allowed me to discover games (I guess mainly Japanese ones?, "Guwange" is an example) I had never experienced in the arcade. I had also missed "Metal Slug" series, happy to discover these games in MAME.
With MAME I rediscovered games I had only briefly seen in the arcades before they were gone: "Tail Gunner", "Omega Race".
I also tried games with MAME I would have passed over in the arcade like "Golden Tee Golf". Really enjoy that one (you need a track ball though!).
MAME did sort of ruin "pay-to-continue" games like "1941". But I sort of hate those games now anyway for having a "pay-to-continue" model.