Hm, I'd like to suggest a Parodius game - the strange space-shooter by Konami that's a parody of the Gradius games. There's a lot of games in the series, but to choose one I suggest "Gokujou Parodius/Fantastic Journey" since I've played that one already and I like that one. It was originally an arcade game, but later got ported to SNES, and also Playstation and Saturn (latter two as part of a multi-game pak). It's a weird, colorful, fun space shooter with a wide selection of characters, each with different attacks.
I'd also suggest Legend of the Mystical Ninja. It's a SNES game from Konami's Goemon/Mystical Ninja series. I learnt about it and the series from Game Center CX, thought it looked fun, and after trying out the game myself, I enjoyed it. So I'd like to suggest it.