Most arcade games were rather shallow! Just a short but hectic amusement ride. When you can keep inserting coins in MAME, the novelty wears off. Still, stuff like GOLDEN AXE, NIGHT SLASHERS, SPLATTERHOUSE or CADDILACS AND DINOSAURS were pretty fun!
Some of them stand out. CHIMERA BEAST is a pretty hectic game where you are a monster who steal DNA from enemies to evolve in the heat of battle.
I can really recommend the original twin-stick shooter
ROBOTRON 2084. Hard as nails, but fair. Requires zen-like focus.
Some games on GOG are sequels or inspired by arcade games:
Raiden IV: OverKill Aqua Kitty: Milk Mine Defender Crimzon Clover: World Ignition Luftrausers BlazBlue Calamity Trigger Broforce Super Puzzle Platformer Deluxe There's also a lot of action roguelikes that has an arcade-ish feel.
Virtual Reality let you get pretty close to the original arcade experience:
Gon' E-Choo! -- Indie clone of the classic Popeye.
New Retro Arcade: Neon -- an engine that let you load MAME roms into actual (VR) arcade machines.
Zaccaria Pinball VR -- recreations of some older, real-life pinball tables. Feels truly authentic.