In the leadup to today, we knew that there would be a way to really customize your Moto X, though it was unclear if carriers would have these options. Most of what we had heard was that carriers would have the choice of black and white and that would be it. So, one of the few surprises today was that AT&T would be offering the Moto Maker
customization options, and that "other carriers" would join the program later on.
The "other carriers" have mostly been quiet about offering the full customization package, but Verizon has confirmed that it will offer Moto Maker later this year. The information was part of a tweet sent out by @VZWnews, which said that the Moto X in black and white would be "coming soon" to the carrier; and, it also confirmed that Moto Maker will be available to customers "later this year".
So, if you really wanted a Moto X on Verizon in eggplant or with a wood grain back plate, it seems that will eventually be an option for you, but it is unclear exactly when you can expect it.