If any 3 points are collinear
One simple way is to fix a point $x$, compute the slope of the line $xy$ and store it in a hash table for every other point $y$. If there is a collision, then we have collinear points involving $x$. This takes $O(n)$ (if we assume hash table operations take $O(1)$). We then do this for every point $x$ in time $O(n^2)$.

Also if you are aware of the point-line duality (please refer to Artium's comment below), this reduces to checking the $n^2$ possible intersections of $n$ lines, but also makes use of hash tables.

Also it is open whether this can be done in sub-quadratic time as this problem is 3-SUM hard, please refer to this answer.