I love the standard SuperNes control pad (Although start/select and the shoulder buttons can fail over time). Also, I love the wireless Xbox 360 gamepad. It's just about perfect besides having a near useless d-pad.
I think my favorite is probably the standard NES controller: very simple, very comfortable, very durable (believe me, I know). I also like the Genesis 6 button controller quite a bit. The original Xbox controller feels nice in my hands, and I love the triggers especially for racing games. In my opinion the Wiimote/nunchuk combo is probably the most comfortable controller. You can pretty much place your hands in any position you want since it doesn't force you to keep them together. I used to like the Sony contoller a lot, but over time I've liked it less and less. I actually do like it a lot for (the very few) games that require the d-pad for movement, but it just doesn't seem to mold to my hands very well.
Nothing has been as cosy, compact and effective to use.
NES I didn't include, it has "sharp sides" which isn't comfortable after a while... but still a fine controller and worth the honorable mention.
I'd also include the Odyssey 2 for being reliable, accurate and easy to use.
Better then Atari 2600, because I felt the rubber over the stick, is too "phat" with the Atari joysticks, and also some of those 2600 joysticks were/are as stiff as a ... BOARD. I said board !
That plastic white stick would not get any easier to push in sharp directions
after years of play...!!! Unless you got lucky and bought one with some give.... also the fire button, sometimes on certain sticks feels like you hit the button twice when you only pushed it once. What's up with that?!
I love the look and design of Atari 2600 joysticks but they are CRAP in general. The domes inside can break suddenly, and so do the wires....
Need to get a controller adapter someday so I can use a more comfortable controller on it. Incidently, how would you save if you were using something like a Playstation controller adapter on a Dreamcast? Do they usually include a VMU slot on the adapter?
The most comfortable handheld is definitely the Game Gear. You've got to experience it to believe it, but that thing is VERY comfortable.