This is due to joysticks getting worn out over time. To fix this problem, if you have Gamepad software (like the Logitech) that allows you to "widen" the dead zone, use it. The "dead zone" is the area on the analog sticks of your controller that it can move without causing the computer to read it as an input. If you make the dead zone really big, that means you'll have to move the analog sticks farther away from the center in order to make the computer sense motion change.

If you use your gamepad a lot, then the analog sticks on your gamepad are most likely very slightly off centered, which is enough for a lot of sensitive software and games that do not have a dead zone configuration (i.e. FFXIV) to think you're "moving" towards one direction.

If you look in the windows Game controller configuration menu (Control Panel --> Devices and Printers --> right click your controller --> Game controller settings --> Properties) if you let the controller rest on your desk, does it look like the example cursors in the control panel are leaning ever so slightly up/down/left or right?