Q. Are wooden crates still used for shipping in this day and age?

Answer

Certainly however since almost all ordinary cargo is now transported in containers you don't see them as often as you used to. In spite of this when you visit ports that deal with project and heavy-lift cargo you will often notice enormous boxes that are being carried in the traditional manner or as ro/ro cargo. The transportation of practically everything is still typically done using wooden containers. As was said in one of the previous answers they can be put together quickly inexpensively and in practically any size or form imaginable and this can take place in almost any place. Wood has the additional benefit of being somewhat more weather resistant than a standard cardboard box which means that it does not need any additional plastic wrapping to maintain its integrity.