Most 3D problems are really 2D problems in disguise. Look for a way to slice things up so that the important parts of the problem are all on a single plane, and you'll find an easier solution.
Multi-variable equations
When you have several equations in several variables, remember to look for ways to substitute a variable out with an expression based on the other variables, in order to get down to a single equation with only one variable. At that point, you can generally solve it and then work backwards to figure out the other variables.
Turning geometry problems into algebra sometimes makes things easy.
Sometimes the constraints in a geometry problem (the stuff that has to be equal) make really nice, symmetrical equations that are a lot easier to work with than the geometry itself. When you're stumped on a geometry problem, look for a way to do this and it might just get you going again.