When dealing with cutoffs, the Q affects the transition of the specified frequency into the slope. High Q values will result in a resonant peak (a boost) at the frequency before the downward slope begins. Low Q values smooth the transition. With guitar and traditional mixing uses of HPF and LPF, I always use a low Q. With synths, the LPF Q helps shape the desired sound and I sometimes crank it.
When dealing with parametric EQ, the Q is the "width" of adjustment - how many surrounding frequencies will be affected in addition to the specified frequency. High Q will create sharp peaks and valleys, useful for notching out problem frequencies. Low Q will create wide adjustments, useful for smoother, more musical boosts and cuts.