CPS-1 and CPS-2 Capcom arcade machines are a goldmine, if you are into beatem ups. Apart from the obvious titles here is more of the titles:
U.N. Squadron
1941: Counter Attack - I doubt anyone didn't stumbled on this title or similar during the 8 bit era. World War II, big aeroplanes, big war ships, it's a total chaos out there.
Carrier Air Wing
Mercs - Imagine old Commando, but with better graphics, and more brutal difficulty.
For the CPS-2:
Street Fighter Alpha 3 - The final alpha SF, massive rooster, lots of diffrent moves, you can spend months on it and it never gets old
Giga Wing - classic shooters, great graphics, lots of explosions. You don't need more in that type of games.
Vampire Hunter 2: Darkstalkers' Revenge (I've never bothered with the first part, since the sequel has everything already)
X-Men: Children of the Atom - I've never liked X-Men, but the game really is a wet dream for the fans of the universe
Capcom Sports Club (Seriously, just try the tennis. This is my favourite virtual tennis game ever. The computer player is really tough to beat)
Battle Circuit (very wacky, funny brawler with strange characters to choose)
Cyberbots: Full Metal Madness (if you like big robots, fluid 2d animations and 1vs1 fight you'll love it)
Armored Warriors - Another big robots game, but this time it's a classic brawler with 3 players max. The awesome future is that you can pick up junk from destroyed enemies and make yourself a new arm or a weapon!
Slammasters II - Japanese wrestling with moves that wouldn't be allowed in WWF, WWE or any other federations
Dungeons and Dragons dilogy is a must of course. You have alternative paths to choose, so the game is still fresh even after you beat it.
Since we are talking about D&D, there is also game called Dungeon Magic. I was really surprised how much effort was put into the game. There are many multi paths to choose, and the graphics, while not gorgeus as Capcom's flag titles, still manages to look good.
Random newer titles, that I still keep on my HD and play from time to time:
Shooters:
Aero Fighters (This is a trilogy, so if you like the first one, go further)
Air Gallet:
Air Duel:
Alpha Mission II:
Batrider:
Batsugun:
Battle Bakraid:
Change Air Blade:
Cyvern:
Daioh:
Darius series:
Desert War - you can choose difficulty and choose how many levels you want to beat up.
Dimahoo:
Dogyuun:
Final Star Force:
Gdarius:
Gratia:
Guardian Force: Instead of a ship we have a tiny little tank that will change gigantic war machines into pile of metal junk. Feels like mechanized version of David and Goliath
.
Gride Seeker:
Gunbird 1,2
Gunlock:
Gunnail:
Guwange: Don't play if you have an epilepsy problems. Just look at random screen.
Hyper Duel:
Mazinger:
Parodius: Just watch out for those BOSS battles.
Raystorm: 3d graphics included. It reminds me of Wipeout due to the design of the ship.
Samurai Aces:
Sengeki Striker:
Shienryu:
Sol Divide: Looks diffrent, as you play some sort of angel of retribution.
Super-X:
Thunder Dragon 1,2
Twin Eagle I, II:
Brawlers:
Golden Axe: Revenge of the Death Adder. Asking if you played the first one would be an insult. This is a rare example of good sequel. It felt longer than the first one, and the audio-video department is top notch.
Growl - you play someone stylized like Indiana Jones. You beat the poachers who want to enslave animals. Many hillarious encounters.
Metamorphic Force - If you played Shadow Caster, you should be familiar with the new idea for this game. You have normal human form and can transform into diffrent animal form that can give you the upper hand in the combat. Nice graphical style.
Warriors of Fate - Koei is producing Dynasty Warriors game in 3d, but Capcom was making something similar way earlier. Check out Dynasty Wars too.
Shadow Force - I must say this is one of the most interesting attempts in the genre. The graphics and audio are cool, but the way that the fighting mechanics are done is more similar to 1vs1 games and you really have to be patient and know when to hit the attack buttons because enemies know how to block and they don't give up easily. In between the regular levels you have a normal 1vs1 fights with the coop buddy or the computer. The final confrontation with the Lucifer is literally majestic, and it's not used in an ironic way.
Night Slashers - This would have been typical slasher, if not for horror theme, where you fight zombies, vampires and other monsters.
Violent Storm - Konami first attempt in the genre. And it blew my mind how good it was when I first played on original arcade machine.
Gaiapolis:
Another Konami production, and another success. Original perspective, not seen in any others titles.
Sengoku 3 - Not strictly mame game system, but it's worth praise nevertheless. Made during the ending of Neo Geo platform life, it brought many new things that weren't see before. You have great, adaptable fighting system, which capable player can use for it's own advantage. You start with a couple of characters to choose, but later on you have an opportunity to change them. Don't ask me why, just play it. Beautiful graphics and animation.
Mutation Nation - needs Neo Geo rom too. Similar to Night Slashers due to the monster types.
The Outfoxies - Have you ever wondered what it would be like to be a monkey hitman wearing a cylinder and battling other hitmans for cash? No, of course not, because it's sounds so ridiculous. It's a mix of Spy vs Spy, Rolling Thunder and Elevator Action Returns. Totally insane game.
Warzard - Strange tournament fighter from Capcom. You only have 4 characters to choose.
Arabian Magic - The Djin is real, and is gonna help you to kick some butts.
Vendetta: Instead of screenshot I will insert here a promo poster.
And now for something completely diffrent:
Goalx3 : GOAL ! GOAL ! GOAL. Fun arcade soccer game.
Time to insert some virtual coins.
I have most of the Mame games, but frankly going through the whole catalogue would be madness. Maybe some other time I will do the whole Neo-Geo catalogue. It's easier to make a whole list of essential titles.