Essential fighters would be KOF '98 ('97 is no slouch!) & Samurai Shodown 2 (as mentioned). For games that are a little dated but still awesome, Fatal Fury Special & Samurai Shodown 1 (which happens to be my favorite game ever). The Art of Fighting games are a little weird, but awesome, and Galaxy Fight is indeed good. These are all games you could pick up in a big stack without breaking the bank, but for the pricier games, definitely Waku Waku 7 and Ninja Masters. Most would say Kizuna Encounter too, but at least that one's available on the 161 multicart. The World Heroes games aren't completely horrible either....if you can get them for $10 or so.
For shooters, hell yes Viewpoint.
For sports games, I personally adore Baseball Stars Professional. I know most would recommend BS2, but I like the team customization in the first one. Neo Turf Masters is also the best 2D golf game ever. Street Hoops is fun, as mentioned (also notable cos the cart music has actual rapping).
For random-ass games, King of the Monsters (a wrestling game) & League Bowling.
For puzzle games, Bust-A-Move (plenty of functional bootleg copies floating around) and either of the Magical Drop games. These will keep your lady friends occupied. (ladies love KOF '97 as well, as it has the most forgiving controls of any KOF, plus Shermie & Mai)
Like I said, these should all be pretty cheap unless otherwise noted, but the Last Blade games are excellent (best looking games on the Neo, even if they're not super cheap).
P.S. Buy Fatal Fury 1 (supercheap!), and don't stop playing it til you like it. The moves are tricky, but it can be very rewarding. It may be simplistic, but the characters hit hard as fuck, so you can tear through it in no time once you get good. Plus, 2 people can gang up on the AI. It was also the beginning of the older games having hilariously weird bonus stages between fights. I miss that.
The recommendations for non-fighters are very helpful too because I don't know much about NeoGeo games outside of fighting for the most part.
