This is my thesis, which at least apparently contradicts what we are given about his character in the released films, but actually seems to confirm some facts and resolve some contradictions therein. Han Solo has the Force.
Let me clarify what I mean. I mean that Han Solo is sufficiently strong in the force that he can perform acts that would otherwise be impossible; that, in Obi-Wan's formulation, he is partially guided by it in his actions but that it also responds to his commands. If Han Solo were younger and had been trained to use the Force, he could have been a powerful Jedi; instead, he simply becomes the last of the Jedis' most important ally.
1) Han Solo does things that are otherwise impossible.
Luke and Vader (especially young Anakin) are remarkable, inventive pilots, as is Lando, but Han blows them all away. In one scene after another in Empire, Han is able to perform feats that Artoo or Threepio say are mathematically near-impossible. He does this in a ship that has a remarkable warp-speed computer but which appears singularly unsuited for close-quarters maneuveurs. Finally, he gets the drop on Vader in Episode IV, and while Vader may have been distracted by his sensations re: Luke, this is still evidence that we are dealing with a very special pilot.
2) Han Solo can communicate with his mind.
Seriously, how are we supposed to otherwise believe that Han can talk with Chewbacca, Greedo, Jabba, and every other alien he meets? Jabba needs an interpreter (Threepio) to talk to Luke, the Princess, etc.; but Solo can talk English to him and Jabba can talk Hutt back? Han's communication abilities fall well outside any "he was raised by Wookies" ad hoc hypotheses. Note that Leia, too, possesses amazing communication abilities, able to impersonate a bounty hunter and communicate nonverbally with Ewoks, along with her ability to telepathically connect with Luke. But Leia's also got the Force, son.
This also suggests that different people strong in the force have different strengths and weaknesss. The Princess is a fair shot in combat, but her strength is in mental communication and resistance to the same. Luke is a great physical fighter, Yoda a manipulator of the universe, Obi-Wan skulks and sneaks around, Palpatine experiments with life, dominates underlings, and deals in pain. Vader can do almost everything, but even he is best known for his piloting ability and his gift for crushing windpipes. Solo can fly, dodge, shoot, and talk to the Universe.
3) Han Solo denies believing in the force, but his denials sound like confirmations.
Han says (I'm paraphrasing) "I've gone from one end of the galaxy to the other, and I've seen a lot of strange stuff, but I've never seen anything to make me believe that there's some all-powerful force controlling everything. There's no force controlling my destiny, that's for sure." At this, Obi-Wan laughs to himself. But the way Han poses the question is one of control. Han doesn't feel bound or controlled by the force, because he can use it, albeit unconsciously. Han doesn't believe in odds; he thinks he's been lucky, but as Obi-Wan says, "In my experience, there's no such thing as luck."
Likewise, there's no way Obi-Wan gets on just any ship willing to take him and Luke to Alderaan. He's played dumb before, but he knows exactly who Han and Chewie are and what the Millenium Falcon is. If he's going to save the Princess from Vader and make it to Alderaan with the stolen Death Star plans and Vader's son in tow, he's going to need a pilot who's strong in the force. And he may have found the strongest.
4) Han Solo has no parents.
This I'm actually taking from Wikipedia's summary of the extra-cinematic books on Solo's origin, but essentially he's an orphan on Corellia. Right in his name, it tells you that he's self-generated. Now, let's see... who else in the Star Wars universe is born into poverty under mysterious circumstances with crazy-ass piloting skills? Now, if you buy the suggestion in Return of the Sith that Palpatine somehow made Anakin -- that is, manipulated the mitichlorians (groan) into bringing him into being -- isn't it possible that Han Solo is another one of Palpatine's experiments? A gifted pilot, strong in the force, strong enough maybe to defeat Vader were Vader ever to turn on him? But this experiment got out of Palpatine's control, the child was lost, to piracy and smuggling, only to turn up one day on the Death Star's doorstep. All five of them -- Luke, Leia, Vader, Obi-Wan, and Han: very nearly destroyed together. Instead, Palpatine is left to play out his Sith triangle with Vader and Luke. Oh well. C'est la vie.