I'm currenty making a bartop with a dreamcast for guts (damn dc games look good on a 14" vga monitor), and am planning to emulate the analog stick with my happs 8-way universal.
DC controllers use hall effects sensors to determine the degree to which a control is pressed (the stick and both triggers); you can ground each sensor to receive the same as a full press. Install a 4pdt switch, and you can flip between controlling the dc dpad and dc analog stick with your arcade joystick.
I'm pretty sure ps dual shock controllers use pots, but perhaps n64 controllers use hall effects sensors.