jwesterman: I have a USB XBOX360 controller and a NES 8 bit original pad hooked up to an adapter and I too cannot controller it's stuck moving my character to the right. I don't like having to use the keyboard.
I use a wired xbox 360 controller, and a fix for me was to make sure that in the options (F10) that the control was set to keyboard, not joystick or any of the other options. I then used a neat little program called JoyToKey which basically tells the computer that your controller's input is to be treated like regular keyboard input. So to put it another way, JoyToKey tells the application that when you press "A" on your controller, the application running (MK 1) will treat is like you pressed "A" on your keyboard. Since you can have all the controls for this game mapped on a keyboard layout, you can map all the buttons on your 360 controller to those corresponding buttons. And because the game is set to keyboard, it will ignore the stick input entirely and you can have total control over your fighter!!! no more random ducking and walking into the enemies!!! YAY!!!
The only downside is that in order to be able to move you have to use the d-pad, and map the d-pad to arrow keys. (I prefer WASD) You could mess around with the stick threshold so that it ignores a certain amount of movement. (in my case it was like a million times too sensitive and if I even breathed to the left the stick would register it a s a full on hard left... so I just LEFT the sticks alone for now ahhaha see what I did there?) On that note, JoyToKey does NOT recognize the trigger buttons, I think because they have some sort of resistor or something to simulate partial depression of the button. (like when you hold it halfway down to free aim in GTA, OR like when you are playing a racing game and don't have the gas all the way down for breaking at corners and such) I could be wrong on that though. ANYWHO...
Every other button you can push will map (right and left bumpers too) I think the middle xbox button doesn't do anything either. So yeah hope that can help you with the 360 controller, I don't know about your other one though... Cheers Mate.