Carton or case is generally used around here, although the high volume of kiwis through these parts often sees the term "crate" mistakingly used. You see, New Zealand has crates; wooden boxes for beer. You exchange your crate when buying your beer this way.
Crates are useful because of the weather. It gets wet, the bottom doesn't fall out like a cardboard box. Beer crates are used for all manner of things such as; shifting house, general storage and for testing the hardness of ones skull 8(
Back when I lived in NZ, the under 21's Rugby-Beer drinking teams of our town were so tough [?] they had competitions where several crates of beer would first be downed before each participant would smash as many crates or parts of crates over his own head as possible without knocking himself out. The winner would get free beer for the rest of the night or weekend. All usually ended up with lumps and cuts and many suffered a degree of concussion (one or two I witnessed were quite serious). Bystanders/drinkers would often pick a favourite and cheer when he staggered or retained his standing. Its little wonder I hardly drank alcohol while I lived in NZ. By comparison, Aussies are far happier, and generally safer drinkers. That's my current excuse anyway
BTW, a certain co-inhabitant seems to think the appropriate term is a "Bluey Box"
