How to quickly tell if a discontinuity is removable or non-removable?

Given any function where you're asked to find all points of discontinuity and to classify those points, is there a quick way to look at it and tell if that discontinuity is removable or not?

-
So, in all other cases, it is non-removable? Like if one or more of the limits (left vs right) are $\infty$? –  agent154 Dec 11 '12 at 2:30
Even of both side limits are $\infty$ the discontinuity is not removable because you cannot set the value of the function at that point to be $\infty$. –  lhf Dec 11 '12 at 2:35