Prusa i3 - All prints are failing, layers won't line up

[GOC]

...it doesn't seem to be temperature related. The actual movements the printer is taking are wrong. I'm using Slic3r and pronterface. Before the print I checked the layers in pronterface and everything looks ok...

- Looking at your images, it seems to be only effecting the one axis in that one direction. When you say "The movements are wrong". I assume that your referring to the extruder head location versus the GCode line its actually on. If this is the case I concur with Mjolinor:

Your axes seem to be slipping. I think it is mechanical so check pulleys and belt tensions. If they are all OK then slow it right down, maybe you are feeding it pulses too quickly...

I would do the following:

• Inspect the pulley/gear & the belt controlling that axis very thoroughly. If unsure, compare it to the apposing axis components.
• Slow all speeds to or below 40mm/s

- If this doesn't help, you may have to consider that it could be a bad stepper motor or motor driver.

Edit: Another suggestion is to also check the stepper and controller wire connections. A weak connection could be present on the wire controlling that axis direction.