As far as what LD is saying, I definitely agree about the GameCube D-pad. Coincidentally, the original GBA's D-pad is the same part.
For comparison's sake, I decided to get a picture of a bunch of controllers and handhelds I had lying around (including a few non-standard ones, which I'll go into for novelty's sake).
In chronological order:
-NES controller. Rectangular. Not very comfortable to hold. Certainly works, though, and incredibly durable.
-Not pictured, but still worth mention: NES joysticks. The one I have, a Honyü Explorer-I, has concave buttons, a big plus. It also features a "slow" toggle, which simply acts as a rapid-fire Start button while on, and turbo settings, including separate rapid-fire buttons and adjustable fire rate. Both are common on third-party NES controllers; the slow button didn't take off, probably because of how dumb it was, but turbo did, and is still present in controllers today.
I use the stick for playing stuff like
Star Soldier, and it works rather well. I also used it when I marathoned platformers a few months back in an attempt to compare
Super Mario Bros. 3 and
Super Mario World. (The better game is
neither of them.)
-SNES controller. A bit more comfortable to hold. Has shoulder buttons. The two concave face buttons are useful for differentiating between the buttons under your fingers when playing games like
Street Fighter II. Also very durable.
-NES2 dogbone controller. I like the NES2, aside from the fact that it only has RF out. The controller is very nice, designed (as the system itself was) to resemble the SNES equivalent. Not much to say about this, aside from that it's far more comfortable to hold than the standard NES controller.
-SNES Super Advantage. This thing needs to die in a fire. Flat buttons in a horrendous layout, and they're prone to sticking. Way too much decorative stuff going on, as well. It also has that dumb slow toggle, including adjustable slow rate (???), and it's designed such that it's in your way and very easy to accidentally press. On the upside, it does feature both full-auto and turbo switches for all six buttons, plus adjustable fire rate.
This controller desperately wants to be used for
Street Fighter II, but its design is so terrible that the only way to really do so involves reconfiguring the controls in-game, which is a bad sign.
-Original PlayStation controller. No analog sticks. Side grips. Four shoulder buttons. Standard Sony face button design. The first iteration of the painful Sony D-pad. Durable. Rather small.
These controllers are good for shmups and four-button fighters.
-Not pictured: a really old EA Sports PlayStation controller I have. It's another pre-analog design, but the casing is rubberized, it has a 360° D-pad (it's nice not having those painful slices in the middle), and the shoulder buttons are a bit different as well. Mostly the same as the standard PlayStation controller; this is the one I normally use for things like
Melty Blood and
Mushihime-sama.
-N64 controller. You all know about this - in fact, I wager most people here would have a stronger opinion of this controller than I do, because I never played the N64 as much as some of the other systems I'm talking about here. My opinion: weird button layout, weird handles, crappy easy-to-break analog stick.
-Also not pictured: the original Dual Shock. It looks very much like the Dual Shock 2 that's sitting there, but they're not quite the same. I'll get to that in a bit.
-Dreamcast controller. Hoo boy...terrible D-pad, terrible analog stick, and more often than not the VMU ended up being little more than a gimmicky memory card. I also never get used to the button layout, especially the shoulder buttons. The controller cord coming out of the bottom rather than the top is something I'm glad didn't catch on. The Dreamcast controller has one neat thing going for it, though: there are little raised dots on each face button, corresponding to which direction that button lies in.
It's a good thing for the Dreamcast's sake that there are a lot of really good games on the platform, because this controller is almost bad enough to turn me away from it immediately. (Coincidentally, the original Xbox controller was largely based on the Dreamcast controller, right down to having memory card slots in the controller itself...)
-Dual Shock 2. I bet everyone here has used one of these at some point or another. Like the original Dual Shock, it features built-in force feedback. Has analog sticks, which click inward as the L3 and R3 buttons. Also has analog face buttons, which the original Dual Shock lacked. The controller in the picture happens to be missing the plastic cap for the R2 button (I think my dad found this controller at a garage sale), but it's still very usable..
As LD pointed out, the analog sticks on these things are terrible to actually try to keep your thumb on. They also have a rather long throw (movement radius), which makes them especially terrible for things like fighting games and shmups. DS2s are probably best suited to games like JRPGs, which don't usually require much in the way of precision. However, I will comment that these controllers are insanely good for twin-stick shooters like
Robotron 2084 and
Geometry Wars.
-
beatmania IIDX Konami Official Controller. Only works with one US-release game! The controller is also very stiff at first, but it's easy to disassemble for things like removing the turntable's spring and placing shims underneath each key. Also, it's not visible in this picture, but you can slide out the key panel to change the layout for left-handed or right-side play. (There's also a little port on the side that resembles a phone jack; it's a holdover from the Japanese version of the same controller. It's so you could plug in a foot pedal for
beatmania III, but they never made a home version of anything from that subseries.)
One of the numerous "you'll use this controller for one game and nothing else" controllers that have come out over the years. They're more prominent with rhythm games, of course, which is why I have several dance mats, multiple guitar controllers, a
Taiko no Tatsujin drum, and two
DJ Hero turntables in my room (more on the
DJ Hero stuff later).
-Game Boy Advance, original model. I agree with CrossEyed and LD here; it's a very nice design. A shame about the lack of a backlight, though. Not really much more to say.
-GameCube controller. As stated before, I agree with LD about the excellence of the D-pad; the analog stick is also decent (it's rubber rather than the N64's plastic, but it also kept the ridging, making it better than a Sony analog stick). The layout of the face buttons can be a bit odd to get used to, but I like them. I'm not a fan of the shoulder buttons, though, and I honestly never got much use out of the C stick. Also, these controllers are incredibly durable.
Then we have a timeskip for a bit (I don't have much of an opinion on the Xbox controller aside from how much of its design was taken from the Dreamcast controller), and then we get to...
-Xbox 360 controller. The reason I'm listing this before either of the two handhelds that technically predate it is because the 360 controller hasn't changed much since its launch in 2005, whereas I have the second revisions of both handhelds, and those both came out after the Xbox 360 did. Anyway, 360 controller...well, I'm sort of new to it, but aside from the D-pad (which easily takes the title of Worst D-Pad in All of Gaming), I really like it. I need to get used to the shoulder buttons, though, and I accidentally hit the guide button from time to time when I mean to hit Start or Back.
-Wii Remote. The only controller I had to remove from a rubber casing. I can't say much about the motion control (don't play a lot of games that use it), and I can't say a lot about the Nunchuk or Classic Controller (don't play a lot of games that use the former, don't own the latter). Most of what I play on the Wii either has you holding the remote like a standard controller...or is insanely better with a GameCube controller. I'm a bit biased due to what I play, though.
-DS Lite. Slimmed down from the original clunky model. Features six buttons and a touchscreen, for lots of interesting control combinations. The system isn't very durable, particularly with the hinge and the shoulder buttons (I bet BP can vouch for this one). Aside from that, it's good.
-PSP-2000. Also slimmed down from an older huge version. Like the DS, features six buttons; however, it doesn't have a touchscreen. Instead, it has an analog nub that is the bane of my existence. The analog nub always feels like it's going to snap under your finger, and the etched top does nothing to improve your thumb's grip on it; instead, all it does it rub your skin raw if you have to use it extensively. The buttons work; the D-pad is a standard Sony D-pad, though slightly better than usual for reasons I can't really describe. Not much to say about this, other than AUGH THE ANALOG NUB SUCKS.
-
DJ Hero controllers. The base on the left without the turntable part attached is for 360, while the one on the right with both turntables attached is for the PS2 and PS3. Designed so that you can detach the turntable piece and connect it on either side of the base, to accommodate left- or right-handed play. The controller is designed specifically for
DJ Hero, of course, and isn't really useful for anything else...but other games are actually exactly why I have the 360 base detached from its turntable part: because the D-pad and face buttons work fine for games like
BlazBlue: Continuum Shift, which doesn't require the analog sticks or shoulder buttons. (Basically: I haven't bought more controllers yet.)