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The King of Fighters 2002 - Fans will argue over whether 98 or 2002 is best. 98 does not have Kula in it, so 2002 is better.
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Puzzle Bobble - If you have a friend to play with, the original is still the best. However, there's no versus CPU, so substitute Bobble 3 if you're playing by yourself.
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Waku Waku 7 - Incredibly goofy and colorful fighting game, every single character is a parody of 90s anime/game tropes.
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Twinkle Star Sprites - A versus shmup with a super unique format.
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Windjammers - A sort of extreme pong.
Also check out FightCade for netplay, many of these games have active communities.