My joystick either keeps pulling to the left, right, up, or down. Also when in the menus, often does the same cycle, putting all of my progress in jeopardy if I miss-time the cycle. It doesn't happen every time I do a mission, but it occurs a large majority of the time.
I'm using two USB joysticks, and both are calibrated, and they both have the same problem.
This problem occurs in both RB1 and RB3D.
Any solutions are welcome!

Are both the joysticks plugged in at the same time? If so try just having one plugged in.

No, I've tried both of them independently and still the same problem.

Not much with JS, but does this happen with other games? and what brand/model of of the joy sticks?
Sounds like you might need to clean them.

Hrm... is this RB1 or 2?
In RB1, this is pretty standard, and happened in the original dos version.
If your joysticks 'float' that would certainly explain it, the cleaning / replacing pots might be worth a try- check it out in the windows control panel.
Otherwise, make sure your joystick is centered at all times, particularly during loading screens... I'm suprised it makes a difference in RB2, but you need to do this in RB1.
I'd stick with just the one, and get that to work first. presumably you want 2 for the added axes...? RB1 seems to think AX 1 and 2 are roll and pitch, but 3 is throttle and 4 is rudder, so it generally gets it wrong with modern 'twist grip' sticks.

Hey I have this problem too in RB1. I find that if i start a mission and quickly presss alt-c, and do 2 or three joystick callibrations in a row it works. other than that you should keep your stick centred during loading screens. hope that helps :)