Separating axis theorem (SAT)
Two convex shapes fail to overlap if and only if there exists an axis along which their shadows do not overlap.
The theorem is a special case of the hyperplane separation theorem from convex geometry, and it makes collision tests surprisingly simple. For two convex polygons it is enough to project both onto a finite set of candidate axes — the normals of each edge — and check whether the intervals leave a gap on any single one of them. Find such a gap and the shapes are apart; you can stop looking immediately.
SAT underlies a large share of 2D collision routines in games, precisely because it is easy to write correctly and easy to debug: the separating axis can be drawn on screen. In 3D the number of candidate axes grows (edge-against-edge adds cross products), and many switch to GJK instead. As a bonus the method hands you how much the shapes overlap almost for free — the smallest overlap along any axis is the penetration depth.