It's also very common, says Tovah Klein, Ph.D., director of the Barnard College Center for Toddler Development, in New York. Babies often begin to show a preference for one parent over the other at around 7 or 8 months -- about the same time that stranger anxiety kicks into high gear. "They want to be with the person who feels most familiar and comforting, which tends to be Mom," says Klein. (But it could also be Dad, as it was for Gracie's older brother Gabriel, now 2.)
If you're the spurned parent, just be patient (and try not to take it personally!) -- this phase usually lasts only a couple of months.