Fighters: Street Fighter Alpha 2/3, Capcom vs SNK 2, and does Smash Melee count? Its technically 2-D. I also like Final Fight 1 and Sengoku as a beat em up.
Platformers: Klonoa(by far), Mario Bros 3, Mega Man 3, Super Metroid, Metal Slug, Cyber Lip.
RPG/Adventure: Odin Sphere(2-D enough for me imo), Zelda: Minish Cap, Guardian Legend
SHUMP: Guardian Legend, Jet Fighters Raiden China Version, Alpha 2 Squardon: Last Guardian, UN Squardron, R-Type.