I'm not much of a fighting game guy and I just snatched a brand/new sealed AES copy of Blue's Journey for a decent price (~$70), just to give you an idea.
No go on RPG really except maybe Crossed Swords which is more or less an rpg, its a first person sword fighting game. As for platformers I really like spin master but I think that can get a little pricey. You consider an mvs to aes converter? That would open the doors to a lot more cheap titles
He mentions MVS in the title but buying an AES cart in the thread, so I think it's save to say he has the facility to play both Spin Master is very good. Top Hunter is decent. Magician Lord is hard, but quite rewarding if you persevere. Nightmare in the Dark is an oft-forgotten gem, rather Snow Bros-esque. Then there's the run and gun games like Metal Slugs, Cyber-Lip and Ninja Commando is one I like - very Ikari Warriors. Surely the only Neo Geo RPG is Samurai Spirits for the Neo CD? Racing, as in driving? Uhh... Over Top? Thrash Rally, perhaps? Then there are the two racing games for the Hyper Neo Geo, but you'll need a Hyper driving version board to play those.
Another vote for Nightmare in the Dark. How about puzzlers? Magical Drop and puzzle bobble / bust a move are great.