Is there a general law for physics?
The principle of stationary action is what you're looking for.
You can construct a quantity called the Lagrangian, which is kinetic energy of the system, minus the potential energy of the system, namely:
$$\mathcal{L} = T-V$$
It is a function of position and velocity and for example, for a particle on a line, with a force acting on it, such that $F = -\frac{dV}{dx}$, you have $$\mathcal{L} (x,\dot{x})= \frac{1}{2}m\dot{x}^2 - V(x)$$ If this wasn't already abstract enough, the Lagrangian is important, because we're interested in its integral from time $t_1$ to $t_2$, namely:
$$\mathcal{A} = \int\limits_{t_1}^{t_2} \mathcal{L} (x,\dot{x}) dt$$ It is called the action, and it's the "thing" nature tries to minimize or, more precisely, to make stationary. What does that mean? Well, it means that, for a particular system, nature chooses such a Lagrangian, which will give a stationary value when integrated between two fixed points.
So, as you might have guessed, the goal of the game is to find the Lagrangian which will minimize (stationarize?) the action.
The Lagrangian for a particle on a line is an extremely simple case, in general it doesn't have to be kinetic minus potential energy and, generally, it's also an explicit function of time, which means that some terms can depend on time not just through position and velocity depending on time.
How to get the equations of motion out of a Lagrangian? You use the Euler-Lagrange equations: $$\frac{d}{dt} \frac{\partial \mathcal{L}}{\partial \dot{q_i}} = \frac{\partial \mathcal{L}}{\partial q_i}$$ What's that $q$? Those are generalized coordinates, they can be Cartesian coordinates but they can be all sorts of different coordinates, whatever works the best.
Try out the equations on my example of a particle on a line.
You might be thinking, why the Lagrangian, what does that have to do with anything and how do we even get them? Well... mostly quantum mechanics and guesswork. After all, classical mechanics is only a limit of quantum mechanics and therefore it has to obey its underlying principles.
Although the Lagrangian is also used in quantum mechanics, there's an even more elegant concept, the Hamiltonian and Hamiltonian mechanics formalism, which basically sets the rules.
Bottom line, you can view it as this: $$\text{constructing a theory} \longleftrightarrow \text{finding the Lagrangian}$$
If you want a classical intuition for why is it kinetic energy minus the potential energy, you might want to read the article "Gravity, Time, and Lagrangians", Huggins, Elisha, Physics Teacher, v48 n8 p512-515 Nov 2010.
Well, there is at least a principle which states that system "tries" to minimize it's energy.
As was also mentioned in comment above, in general I believe there is just Principle of least action, from which one can also derive conservation laws which are neccessary consequence of Lagrangian symmetry - Noether's theorem. (Action is integral of a Langrangian over time).
Although there's no consensus, I think that the vast majority of my physics colleagues would answer your question with a "yes", but acknowledging that we don't yet know for sure what that general law (jocularly referred to as the "Theory of Everything" or ToE) is. The above-mentioned principle of least action is a good start, but it's not the final word, since it's for classical physics only. It can be elegantly incorporated into quantum mechanics using a mathematical tool known as the path integral, but we physicists as a community have still not succeeded in unifying quantum mechanics with Einstein's general relativity into a theory of quantum gravity that we can fully understand and test against experiment. String theory and loop quantum gravity are two popular competing contenders, but the jury is still out.
Schlomo Steinbergerstein mentioned a stone-age paper of mine discussing these issues, but I discuss all this in much more detail in my new book http://mathematicaluniverse.org