One thing I had to learn when I moved from short stories to novels was how to write subplots. A short story generally carries only one plot line, and I wrote a bajillion short stories before concentrating on books. This may be why I tend to have a strong through-line in my books. While I'm drafting, I don't usually lose sight of the plot by taking too many detours. My trouble tends to be in the other direction: building in those subplots, fleshing out the book so that it's more than a skeleton.
I remember discussing subplots with one of my earliest critique partners. At the time, I said I thought that the subplots should relate to the main plot somehow, either by reinforcing it or providing a mirror image of it (perhaps an alternative or road not taken). Now I believe that even more strongly. It's best of all when the resolution of a subplot has a critical effect on the main plot. (Holes by Louis Sachar is a masterpiece in this respect, with multiple subplots providing key puzzle pieces for the plot.)
Subplots can also provide comic relief, with side stories that may be lighter than the main storyline. They can give us a chance to see into the worlds of secondary characters, rounding them out a bit more.
I don't consciously plan out subplots. In fact, the sketchy not-really-an-outline plan from which I write a first draft focuses exclusively on the main plot. But as I write, I feel a natural rhythm to the piece: wherever the story needs a breather, or where an interesting limb pokes out that looks as if it will support the weight of a side story, or when a secondary character starts demanding more stage time, I see the potential for subplots. One of my biggest jobs in revision is usually editing the subplots: rearranging their components, enhancing them or pruning them back, taking care about where they intertwine with the main plot.
How do you handle subplots?