The arcade, though once the hub of videogame culture and bleeding edge of videogame hardware, has since dwindled in popularity in most parts of the world. And the arcades that are still to be found are mostly dedicated to a few select genres. Luckily we have MAME, which does a good job of emulating the wide variety of arcade hardware, even if it can't simulate the variety of input and feedback features that still make arcade cabinets special. Not to mention the atmosphere of the places. There have also been some good arcade compilations for consoles. Particularly worth mentioning are the Sega Ages series, and the Taito compilations. There are some okay Midway ones too, but not all the ports included are great. It seems like companies are getting a bit better at putting them together, at least; and a bit more generous.
This section is potentially quite large, so things are organised into loose genres.
Uncategorisable, and as-of-yet unsorted. Probably a good group of arcade games will fit here.
Beat 'em ups, Belt Scrollers, and other games where one wanders the screen terrorising hordes of palette swapped punks. One of the big genres in the heyday of the arcades: big colourful graphics, multiplayer, and great soundtracks are typical genre markers. There are quite a few gems that never made to to consoles, too.
One of those genres that are a bit tricky to port to consoles. Though ports and gun accessories were quite popular during the 32-bit era and on the Wii, some of the more attractive features—like big unique guns, strong force feedback, etc.—were never able to make the transition.
(The scope of this classification is probably too large; it pretty much encompasses every early-earlyish arcade game, and many later ones. Single-screen platformers could have their own bit, at least.)
Another one of those genres the arcades really do well, which is why you'll still find linked Daytona cabs. everywhere.
Racing games viewed from overhead perspectives, typically made in 2-D, and having large portions of the track in view, if not all of it.
For games with 'cockpit' or behind car viewpoints, be they actually 3-D or not.
unlabored flawlessness: I find its very short, heavily downsampled music loops rather hypnotic.
Honestly, it's less stressful than most of the Irem shooters it rips off. What happened to Allumer, anyway?
Railshooters, Hariets, and other 3-D, into the screen type shooting games. Often the arcade versions have big moving cabs like racing games.
Now the main arcade genre, and one who the arcade experience is still considered a vital factor, even during development (IE the importance of location testing). Make sure to browse the CPS and Neo Geo pages for lots more.