Famicom BPS-Max controller. In the US, the Max was a first-party Nintendo product, but, like the Power Pad, it originated as a third-party device, originally sold by Tetris publisher Bullet Proof Software.
I don’t know how people feel about the Max these days, but I love everything about it — the grips, the tiny size, the unique and almost completely pointless disc-based D-pad. As far as I know, the Max stands alone in that design, which probably says a lot about how other people feel about it, given the influence every other Nintendo controller had on future generations.
More than anything, I love the dedicated turbo buttons.
This new-in-box BPS Max (for use with Famicom only!) is available on eBay for $40.