One of my favorite platformers of all time (in fact, probably number 1 after all the Mario ones, and ahead of some of them already) is Plok on the SNES. A little yellow and red guy who attacks by shooting his limbs at enemies. A lot of the game is named after sewing terminology, for some reason (Cotton Island, a boss fight against the Bobbins Bros., all in the archipelago of Akryllic), as just another of the game's quirks. Has a lot of personality for a SNES platformer. Considering it has no save or password (which the creators admitted was one of its greatest flaws), it's a bit long, but if you're going to be playing it on an emulator (it won't be out on the VC for a while, if ever; the Pickford Bros. own the rights to the character, but whatever company bought out Tradewest owns the rights to the original programming, and they haven't gotten around to talking to each other yet, so neither of them can do anything with the original game right now), it's not much of an issue. And the music is beautiful. Excellent use of the SNES's sound chip.
For a more recent game, you should really go out and buy Blast Works for the Wii as soon as possible. I haven't had much time with it yet, but I've had enough to see the amazingness. The main game is like a cross between Gradius and Katamari. It's a side-scrolling shooter, and when you shoot down enemy planes, you can catch them with your own plane to attach them on, and they'll start spewing out more bullets at your enemies from wherever they are. Even parts of the bosses can fall off and get attached to you. When you're not playing, you can customize basically everything. You can make your own levels, ships, enemies, bosses, and weapons with some really powerful, but still pretty graspable editors.