User interfaces don't make much use of relative mouse movement at the moment -- other than the odd knob-like adjustment tool, or gestures (which I've never been terribly convinced about as a UI concept). Given that laptop users are often forced to use an inherently-relative trackpad (or occasionally a stick) instead of a real mouse, it'd be useful to minimise the amount of fiddly absolute positioning necessary in mouse-based interfaces.
A mostly-keyboard-controlled window manager could use relative movement to shuffle windows around: you press a number key to select a window, then drag it to its new location using the mouse. This more than halves the distance you have to move the mouse, which would be a great advantage on a trackpad.
A text editor could use mouse or scrollwheel movement to adjust numbers in text, using a logarithmic scale so that it wouldn't matter how big they were to start with. (Or log vertical and linear horizontal, or similar.) This'd be great for a live-feedback TeX editor.