They do make wedding cake delivery boxes that are sturdier and larger than standard bakery boxes. They are more expensive, so you'll want to make an effort to keep them clean so you can re-use them. Global Sugar Art carries them (as do a lot of other cake supply sites). You can check them out at:
I never use boxes I just put down shelf liner in my trunk. If I am putting the cake together on site I do use the bakery boxes for each tier. The ones GSA has are nice