What gazelle says here makes sense. Another example is UP. We know that Russell’s father is divorced, and that he’s still alive, because Russell talks about how he tries to call him but the new wife doesn’t let him talk to him because she thinks he (Russell) bothers him too much. Although Russell’s father is not really a character in the movie, we are told what became of him because it’s an important part of the plot - which is how this lonely boy and lonely old man come together and bond. Andy’s father doesn’t have this kind of relevance to the plot of Toy Story, so even though I’m curious about what became of him, I can understand why even the story writers don’t know the answer.
I’m with those who believe that he died, and I think he died shortly after Molly was born. But I think that he gave Woody to Andy long ago, when Andy was little.
As a kid I always thought he was at work or something, but now it occurs to me that anything could have happened. They NEVER mention him. Is this single-parent thing a Pixar trademark? Russels’ mom, Andy’s mom, Marlin, the Queen in Bug’s Life…oh and Linguini’s mom! I agree with Dragonrider, maybe Andys father died, and gave Woody to Andy, which is why he’s so important to him. Or the reason why they were moving in the first one was because the parents split and the house belongs to the father. Or something.