People need to stop saying that the Neo Geo is practically a "fighting game only" system and realize that there is more to the Neo Geo than fighting games, even though it does have a good share of them (and I don't see how SNK's fighting games wouldn't appeal to people that play fighting games). The following is a small list I have constructed of some non-fighting Neo Geo games that new comers to the Neo Geo may enjoy:
Magician Lord - Excellent platform game and even though you get infinite continues, it gets to be pretty challenging and requires some thinking to find where to go. First Neo Geo game I ever played actually.
Windjammers - This game is so addicting, especially if you have a friend to play with you. Me and family members really get into this game and have strong competitions. It's kind of like Pong, but with really unique and original twists.
Crossed Swords - A bit cheesy, but it's a fun first-person viewed adventure with RPG elements and a total arcade feel. Really fun to play through once with a friend.
Blue's Journey - A fun, cute, colorful platform game with some creative ideas. It's a pretty fun game.
Cyber Lip - Before Metal Slug, this was a platform shooter for the Neo Geo. Though it's not as extreme as Metal Slug, it's still a great old school style platform shooter or run n' gun game.
Sengoku - The first game of a triology beat'em up series for the Neo Geo. I forgot how this game was exactly, but I know it's fun and was pretty original. The sequels are pretty good too.
Top Player's Golf - I know, a golf game. But for some reason when I first started getting into Neo Geo, this was one of those early games for me and I love the game! I don't know what it is, but this game just feels so fun and relaxing for me, unlike most golf games.
League Bowling - This game is just plain addicting!
This is just a small list and they are all older games for the system, but their fun classic games that classic gamers will appreciate.