Well there are two explanations:
Using the anthropic principle, any object that did NOT have a stable orbit would either have impacted the sun or been lost to space. So obviously anything thats left would have a stable orbit.
Its a catch-22 and it works, but its not really an explanation.
The eplanation is in planetary formation - the planets condensed from a disc of gas and dust that was rotating. As it collapsed from gravity, it rotated faster, eventually reaching a sort of equilibrium of density and rotational rate from which the planets condensed.
And *YOU* do!!!??? Well damn, lay out your theory to replace QM, then hop a plane to Stockholm to collect your prize! Or maybe the alternative - *YOU* do not understand what probability is and how it relates to physical reality.
Oh the irony. Wasn't it you who spent 20 pages in another thread trying to show that math does NOT represent physical reality? And btw, those "pet theories" are the ones accepted by the best minds in physics. I'm not going to bet money against Einstein or Heisenberg or Planck any time soon.
Now despite all this, I *DO* think there may be something to "Bode's Law". "Bode's Law" itself is simply a numerical pattern and not an explanation of anything, but I'm thinking that if you look at planet formation (the density pattern of the initial disc), rotation rate and tidal forces, planets formed in the size and location that they are in now for a reason. It would not surprise me at all if we found other solar systems that look exactly like ours. And I must point out that the solar systems we found don't look anything like ours because the means we have to look for them can only find solar systems that look nothing like ours. Most extra-solar planets were found through gravitational perturbations and light intensity fluctuations in stars - and only large planets with small orbits can produce the effect we need to detect them.
Yes, the planets DO all effect each other. Jupiter being the largest has the largest effect - its believed that tidal forces from Jupiter are what kept the asteroid belt from condensing into a planet for example. Also, Pluto (and maybe Neptune?) were predicted and found by observing perturbations in the orbits of nearby planets).