Your favorite videogame controller(s)!

[The Almighty MegaMan]

One of the biggest reasons why I have always preferred console gaming over PC gaming (moreso 5+ years back) are the controllers.
Sure, these days you can use a 360/PS3 one in your computer, even a Wii one if you've got a bluetooth thingy, but up to the days of the Gamecube, every console had a special joystick/pad/controller.

To me, every controller brings forth a different gameplay experience, and there are better ones depending on the genre you're playing - such as the Saturn pad for shmups and 2D fighters, the PS1 for 3D adventure games, etc.

What are your favorite ones? Why?
(A bit of emphasis there because I'm not trying to make a list, rather, I want people to discuss which ones were the nicest.)
Which is the oddest/most rare you've ever come across?