Would a planet in a binary star system follow Kepler's Laws? I'm thinking it would not.  I am thinking Kepler's Laws were a simplification that were possible with a simple two body (sun, planet) but would not apply for something more complex (sun1, sun2, planet).
Is there a more general form of Kepler's Laws that would apply to solar systems with multiple suns?
 A: I like Kieran Hunt's answer but I'm going to give a different answer, even though I agree with what he said.
In a very real sense, our solar system doesn't obey Kepler's laws because there are many bodies.   The planets and even more so, the moons in our solar system don't precisely follow Kepler's 3 laws, but they mostly follow it pretty close.    Our moon has a pretty strange, wobbly orbit since it's pulled on by both the sun and the earth.   But the planets in our solar system do follow Kepler's laws well enough for Kepler to have tested and verified his laws.
In a binary star system, the end result is likely pretty similar.   Imagine if Jupiter was a star - further out.   It would depend on how big and how close, but if it was far enough, the earth could still orbit the sun, while Jupiter and the sun orbited each other.    There's 2 main types of binary systems.   One, where the stars are close and the planets orbit the center of mass of the 2 stars.    The other, where the stars are far enough apart where the planets can orbit either star individually.   See picture below:

Source:   http://jenomarz.com/designing-a-planetary-system-extension/
Now, is this always the case?  and, can I swear that the author of that is right?   Well, no, but I'd wager that, more often than not, even in a binary star system, planets will still largely follow Kepler's laws of 2 body orbits in one of the 2 examples in the picture above.
The problem with 3-body mathematics in a solar system that's been around for a billion years or so is that, the chaos and unpredictability doesn't stay in the system that long.  The smallest of the 3 bodies would likely get cast out or it would likely crash into one of the other 2 bodies before too long or it would find an orbital resonance.   A long lasting 3 body system would likely have a sun-earth-moon stability to it, or a Sun-Neptune-Pluto stability to it or maybe a Jupiter, Sun, L4 or L5 orbit.   The instability of the 3 body problem that has been a puzzle for mathematicians for centuries probobly doesn't last very long in solar-systems.
Edit, I do want to add, that L4/L5 orbits in relation the smaller star in a binary system is likely an additional scenario we'd see depending on the size ratio of the 2 stars, but a stable L4 or L5 orbit is kind of similar to a Kepler orbit.   
There's kind of some mathematical laws for some 3 body problems, not all, I think, and they're very complex.  Lagrange-Euler being the one for L4-L5.   Bit over my pay grade.
Another way of explaining this is a principal in chaos theory called islands of stability or chaotic attractors.  I'll let this link explain that cause I think it does it quite well.
http://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/

While you find that no real life N-body system orbits are stable
  (exactly repeat themselves), you do find that they settle into
  patterns.  For example, while the system of Jupiter’s innermost moons:
  Io, Europa, and Ganymede, never quite repeats the same path, they do
  manage to “resonate” with each other and settle into a rhythm.  Hence
  the name; “orbital resonance“.

So, even in a binary system, you'd mostly see the general predictability of Kepler's laws.
Here's a pretty good image of the unpredictability of the 3 body problem, but you'd probobly not see orbits like this very often.

Source: http://en.wikipedia.org/wiki/N-body_problem
Small point to add, but it's mathematically possible to create alternative possible solutions to the 3 body problem (the figure 8 for example), I don't think it's going to happen very often in the universe.   The figure 8 or the ball of yarn don't follow Kepler's laws, obviously.   
http://news.sciencemag.org/physics/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem
A: If the planet was at a much greater distance from the binary than the distance between the stars themselves (say 10 times) its motion would would be similar  to a Keplerian orbit around a star equal to the combined mass of the stars and situated at their centre of mass.  It has been shown that such an orbit is stable indefinitely.  There would be very small periodic perturbations due to the movement of the stars and the perihelion of the planet would advance, unlike in a pure Keplerian orbit.
      If the planet orbited just one of the stars and the other was at a large distance (again, say 10 times the planet-star distance) the situation would be similar to the earth-moon-sun system with the planet playing the role of the moon, the earth the role of a star and the sun that of the other star.  The huge discrepancy in masses does not matter provided the relative distances are large enough and again the system is as stable as the earth-moon-sun-system.
