Getting a hold of these games might be difficult and costly; the NeoGeo was very expensive at the time because it literally brought arcade hardware to the living room, but you will NEVER see a better looking strictly 2D/16-bit console in your entire life. It is quite possibly the most sought after 'retro' home console with the largest cult following, thus making it highly collectible.
Even still, you can emulate Neo Geo games with Neo-RAGEX which uses dumps from the home version, but you're probably better off getting the MAME version of these games with Winkawaks/Nebula for optimal compatibility or MAME itself. They all come with Netplay; most of these games are multiplayer and will let you quickly jump in, being arcade games and all, try them with a friend. If you're not emulation prone, many of these games come in collections on the PS2, as well. Or if you're just plain cool, you can get a NeoGeo MVS, or get an MVS converter, or even a Supergun as the games are exactly the same only THEY'RE NOT THAT FUCKING EXPENSIVE. Like seriously they cost less than half of what most games go for, and like a quarter of rare games.
Totally fuckwin shmup game. Eight planes, two players to kick ass with, gorgeous graphics and scenery, and fucking awesome old school blowin' da fuck outta everything. Much better than it's predecessor and sequel, and one of the best shmups on the Neo Geo AES.
Alpha Mission II / ASO II: Last Guardian
Shoot 'em up
Early Neo Geo shmup, it features a Xevious style gameplay with a forward shot for aerial enemies and a bomb for ground enemies. You can collect items which grant you various different temporary power-ups which boosts your firepower or defense. Gets quite insane later on.
Art of Fighting (series)
One of SNK's early fighters, the Art of Fighting series features huge sprites, a power bar which is used for every move, a taunt button which decreases the opponents power, and an amazing soundtrack. 2 is a huge improvement over the first game, while the third game is quite a departure from the older ones, featuring all new characters and a rushing combo system.
Baseball Stars 2
Incredibly expressive characters collide in this battle of the sports titans! While it lacks the custom teams of previous "Stars" titles, it easily plays the best, being smoother, faster, and more spot-on. There's still some variables though, as the players' expressions are also an indicator of their current state. If someone's tired, time-out and swap out! There's also the "POW Bat", which does just what you'd think it would when it hits the ball.
Baseball Stars Professional is an okay alternative, but can't really capture the fun-tastic, face-punching feel of this. It's not bad on its own though.
The spiritual sequel to Pulstar, quite easier, and still as beautiful and fuckin' epic.
The best fighting game you never ever heard about! It is a solid fighter with big and fluid sprites and fast-paced action, all you'd ever want in a fightan!
There is an Arcade-only update called Breakers revenge, which adds a new character and changes some minor things.
Beat 'em Up
The best beat 'em up on the Neo Geo, similar to Streets of Rage that shows off the Neo Geo's power quite well.
Hack 'n Slash
Awesome Hack 'n Slash game with a behind-the-player perspective similar to Punch Out. You can slash with your sword, defend high and low and use magic spells. In between stages you can use your acquired gold to buy new weapons and items.
Run and Gun
One of the earliest Neo Geo games, it's pretty much a cartoonier Contra. Doesn't really show off the system's capabilities, but it's still a fun game. This one is worth playing for the ending alone.
The game of the movie of the game. Unlike Street Fighter The Movie it doesn't use digitized sprites and merely takes some elements from that horrible movie, like the Lee brothers being able to transform during the fight and the Terminator guy serving as the final boss (except he looks badass here and not that ridiculous dork from the movie). And unlike that dreck for the SNES based on that ridiculous cartoon, this game doesn't suck. The characters include Double Dragon veterans along with original characters for some solid fighting action.
Fatal Fury (series)
Probably the most famous SNK fighter after the KOF series. The Fatal Fury series main gimmick is the plane switching, which works as a dodging maneuver. From the second game onwards you also have the Desperation Moves, which you can use when your lifebar is low. Fatal Fury Special is generally considered the best from the early games, though 3 is also very good.
Garou: Mark of the Wolves
SNK's answer to Street Fighter 3. The last game in the Fatal fury series, to date, while technically serving as the first in a second series. Features a form of parrying and the ability to choose when you want to be able to use Super Combos. Sequel in the talks, but nothing confirmed to date.
(Possibly the best game on the system!)
Joy Joy Kid / Puzzled!
Tetris with a twist: you must match the blocks to release the balloons trapped at the bottom. By matching blocks you also accumulate power to unleash a energy ball of destruction, which is very useful to get out of thigh spots, but must be used carefully, since it takes a while to recharge.
Karnov's Revenge / Fighter's History Dynamite
A vastly improved sequel to the original Fighter's History (being on the Neo Geo hardware probably helped). Forget everything you heard about this being a Street Fighter II rip-off, because this one is a excellent fighter on it's own, with fluid movement, lots of combos, and a mechanic wherein you must hit the opponent a few times in a specific spot to dizzy it.
Beating the game without losing any round grants you an extra match against the Ox from Karate Champ!
King of Fighters '98
A dream match that features a ton of fighters from previous entries. Features many characters with many styles of play. The classic is still great, but at this point, you might consider the Ultimate Match version on PS2 instead, which has much more content.
King of Fighters 2000
The last KoF developed in-house before SNK's bankruptcy. It's the best of the NESTS Saga ('99-2k1), which featured Strikers, a fourth tag partner that can be called in for an attack a la Marvel vs. Capcom. This game features tons of characters from other SNK titles like Metal Slug's Fio and Kaede from The Last Blade as exclusive Strikers, making this a fan favorite. Later ports to Dreamcast and PS2 add more Strikers.
(Yes, the box-art for this game was sideways).
King of Fighters 2002
A dream match among King of Fighters characters old and new. Even more than 98, although a few characters have been altered, which warrants 98's inclusion. The Unlimited Match version has even more characters (with the old 2k2 ones, this reaches 66!) and is out on Japanese PS2 and also on the 360's Live Marketplace in USA as well.
Kizuna Encounter: Super Tag Battle
More SNK fighting, on my Neo Geo?! Well, sure, why not! You and your opponent can swap characters in the heat of battle, but the match ends when one is downed. Plays most similarly to Real Bout: Fatal Fury (Kim Sue Il even plays a bit like his ancestor Kim Kap-Hwan!), but has the rolling mechanic from King of Fighters, and also some of the hardest bosses known to date (Zero sec. reaction time :P). European release of this is extremely rare and rumored to have sold for $10,000 in 2006.
The Last Blade 1+2
The Last Blade games are well-loved for their incredible gameplay, and are a shining example among fighting games. There is also an EXCELLENT NGPC port that mixes aspects of both games, though the console experience is always best for the full visual experience.
Sports / Casual
Bars, malls, arcades, convenience stores, this game was damn near everywhere back in the day! If you don't know about it, here's the roll-down:
It's bowling, that's it. Time button presses, move the bowler, and knock the pins down. "Why's it so well-loved then?!" You play an extremely schizophrenic bowler who snaps back and forth from panic attacks to being cocky as fuck. Between the bowler and the score screens, there's a lot of expression and animation for a 1991 game. In addition, 4 people can take turns and play in 3 slightly different scoring rules. Great pick up and play fun, and plays surprisingly better than you'd expect! You can even choose your hand and ball weight preference, and save and load them to and from the Neo Geo memory card!
Magical Drop 3
Puzzle Match-# formula, but involves holding and stacking mass numbers of orbs at a time. Also has "bomb" orbs, which clear entire colors off the field. Has some weird and funny character interactions as well.
Cool platformer by ADK, you play as Elta and must retrieve magical books. You can shoot in all directions and collects power-ups which transform your character and grants him new powers.
Matrimelee: Neo Power Instinct
One of the weirder fighting games you will ever play that's actually good. Has a cast of all sorts of people, ages, and fighting styles and also features a few characters from Rage of the Dragons. This game is legendary for having a cheap as fuck last boss (even among SNK bosses), the infamous Princess Sissy.
Metal Slug: Super Vehicle-001
Run and Gun
Animated platformer-esque run and gun with mobile tanks. Also has lots of weapons, such as heavy machine guns and "raw kit lawnchairs". A bit basic compared to later entries, but you seriously need to play this one first to get a feel for the games and understand the in-jokes in the sequels.
Metal Slug X (2)
Run and Gun
The first to include female team members Fio and Eri. Now with more weapons, BIG mode (makes you fat and alters your weapon's mode of fire) and mummies. X is essentially a re-mastering of 2, so it is recommended to play that one instead. Again, you should really play this before 3.
Metal Slug 3
Run and Gun
More of the same, now with subs, airplanes, aliens and zombies. The longest of the MS series and all but agreed to be the best. This is what you've been waiting for.
Metal Slug 4 and 5
Run and Gun
More Metal Slug! The 4th has exclusive characters to that game and the 5th has Sliding. Both are made by a different company so opinions are mixed. Both are still generally cool though.
Beat 'em up
While this may seem like yet another run of the mill brawler, the freaky enemy designs, solid graphics, and the cool soundtrack make it worth playing.
Run 'n Gun
This game came along with the Neo Geo, so there was no reason to not play it! It is a Run and Gun game similar to Cabal, where you control a crosshair to shoot enemies in the background while dodging enemy fire. Unlike Cabal, the screens auto-scrolls, so you must keep on your toes.
BEWARE THE FINAL BOSS! If you lose to him it's an automatic game-over!
Bomberman for the Neo Geo! Nice Neo Geo quality graphics and music. Too bad it's only 2-player!
Run and Gun
A top down run and gun where you play as ninjas.
Ninja Master's: Haō Ninpō Chō
A solid fighting game by ADK, and one of the rarest Neo Geo titles.
Shoot 'em Up
Very similar to R-Type (rumor is that some former Irem people did it), has some really nice pre-rendered computer graphics.
Rage of The Dragons
A Double Dragon spinoff/homage. Features the Lees (now the Lewis brothers) and Abobo along with many new characters. Has a neat combo system where you stun your opponent then input a set of buttons quickly to deliver a quick chain assault.
Real Bout Fatal Fury / Real Bout Special / Real Bout 2
The later sequels to the Fatal Fury series, which reworks the plane switching and refines the gameplay, making it faster and simpler.
Beat 'em Up
A good looking, fast paced beat 'em up that uses lots of scaling effects.
Samurai Shodown I-V
Samurai and other fighters of various backgrounds face off in this fighting game. Features two different styles of offense (typically: one's more speed-centric and the other leans toward power). II is considered to be the all-around best one, though you may favor certain aspects of later releases.
SNK vs. Capcom: SVC Chaos
One of the only crossover games to appear on the system. Plays similarly to Capcom vs. SNK, although with a few differences.
Spin Master / Miracle Adventure
A sort of Joe and Mac spiritual sequel. Uses many of the same concepts, but set in a more modern era. Nice for quick pick up and play, and it's accessible (easy) enough to play with anyone: Kids, friends, family, etc. Just be sure to press "A" at the ending! Pretty fun ride overall.
The characters also appeared in "Dashin' Desperadoes" for Genesis. It controls a bit differently and is a sort of platformer/racing hybrid that changes up when played with 2 players. You might also consider trying that out as well.
Super Dodge Ball
Another sequel in the Super Dodge Ball series. However, it's very fucking fun. Widely regarded as being the best in terms of pure action (as in sans customization and RPG elements) of the series due to a huge variety of moves to pull off.
This entry is infamous for being EXTREMELY rare as it's one of the last games Technos made before their end (and eventual rebirth). The box pic at the left may be the closest you ever get to it IRL unless you have over 500 bucks to throw down.
Super Sidekicks 3: The Next Glory
Another pretty well-known entry of a well-loved series. Sidekicks 3 is probably the best of the series. It's essentially a remastered version of 2, but with even more teams, and different types of tournament cups. These cups are regional, thus giving you a good idea of which countries you'll be facing off against. This series ate many a quarter around the world in its hayday, so you know it kicks some serious grass.
Top Hunter: Roddy and Cathy
A platformer that has plane switching, fighting game input attacks, and stretching arms to hit, grab, and throw stuff. The order of the first 4 worlds is chosen by you. Also on: SNK Arcade Classics Vol. 1
Twinkle Star Sprites
Cute 'em up / Puzzle
CUTENESS OVERLOAD~! A cast of strange characters compete against each other for the prize of a wish from the great Twinkle Star. Combines fixed shooter and puzzle elements for fast-paced competitions between players. While there is single-player, this game was MADE to be played with a friend!
Waku Waku 7
Another whimsical fighting game made by Sunsoft. Filled with parodies of anime and game architypes, even including a guy who's a spoof-mix of Joseph Joestar and Indiana Jones. A sort of sequel/spinoff of Galaxy Fight. Had an air-based spiritual successor in Astra Superstars, which you might also consider.
Also on Saturn!
Sports / Fighting?
A fun take on Pong/Airhockey. Throw frisbees around 1 on 1. Better than it sounds. There's special moves and bonus stages to spice things up. Each character also has different specialties and stats. It's almost like a fighting game in that regard, though scoring goals is top priority.
Shoot 'em Up
Amazing shmup with a isometric perspective, with amazing graphics and music!
Similar to Bubble Bobble, and even more so to Snow Bros.