My favorite statement in classical physics is that light is an electromagnetic wave whose speed we can predict from experiments with charged pithballs and current carrying wires!
My favorite statement in relativity is that a static electric field will also have a magetic component when viewed by a moving observer!
Quantum physics has so much predictive power that I cannot possibly choose just one prediction, but the most mind blowing result for me is that because of quantum mechanics the universe violates Bell's inequalities!
I really like the positive spirit of this thread, buy I found Cyrus' post to be so disagreeable that I have to spoil the thread with the following argument:
Everything is derived from this one equation [F = ma].
Hmm, how do you go from Newton's 2nd to Maxwell's equations?
In relativistic quantum mechanics the maxwell fields pop right out of the principle of locality together with the U(1) gauge symmetry of the wavefunction (i.e. the statement that quantum states are only determined up to a phase). In this sense, the quantum version of Hamilton's equations (i.e. Dirac's equation) does allow you to derive E&M.
It is the most powerful equaiton in all of physics, and it's absolutely non-intutive.
The logical basis for F = ma is almost never presented, although it is in fact quite simple. If the current state of the universe, the collection of all positions and velocities of all particles, is sufficient to determine the universe's state at a later time, then in particular the second derivative must be determine by those positions and velocities:
x'' = F(x,x')
The concept of "force' is superfluous; the empirical task in mechanics is to determine the form of F(x,x'), e.g. Hooke's law F(x,x') = -k x . Obviously the theoretical task is to determine the motion given knowledge of F(x,x').
I challenge you to find a physics book without this equation in it.
How about Howard Georgi's "Lie Algebras in Particle Physics." Heck, there are entire books about classical mechanics at an advanced level that do not mention Newton's law e.g. http://www.worldscibooks.com/physics/3905.html".