The one I love the most would be a mix of the PS controller (Dualshock) and the Xbox 360.
The triggers in the PS controller are not as good as they could be, and the D-pad on the 360 are horrible. For some games I'd rather use one, or the other.
But since we are talking about favorites, I just share my
downright most horrible controller ever.

Let's begin:
1. D-pad, so small, stiff and it looks like a tumor, I don't know, it seems like it's dropping from the controller.
2. Analogs: who came up with the idea of puting an octagon ? what's the point ? Isn't these analog capable of much more subtle movement than simple 8 directions ? I know for a fact they are. So why why an octagon, not only it doesn't look good, but it troubles you gaming experience sometimes.
3. Triggers: Not as clunky as the PS controller but still terrible. Why only SEGA (Dreamcast) and Microsoft (Xbox 1 and Xbox 360) got it right ?
4. Button placement: This is the
"coup de grâce" for me.A big
A button with the other buttons clustered around it ? Why ? To make it harder for you to play ? Couldn't they just copy Sony, Sega or .... THEMSELVES ? Yeah, The Super Nintendo controller was pretty good, wasn't it ? B A X Y placement of buttons was so damn good that everybody copied it, EXCET Nintendo themselves.
Bottom line, the gamecube was just meant not to be a succes like the other Nintendo consoles, if a single thing as the controller couldn't be done right, I can't imagine what they were thinking. Maybe Miyamoto was seek when they planned it and somehow the other people screw it up ... Not to mention the horrible design choice of using mini DVDs as a media format, but let's not go that far or else I'll write forever.
Favorite: PS360
Most hated: Gamecube