We're trying to decide how much effort to put into ensuring that our software works well in 32-bit mode. (It's scientific software that must handle large datasets, so ensuring that it works well does not only mean building universal binaries, but also designing around address-space limitations.)
Q: In what year were the last Macs sold that, out of the box, could not run 64-bit applications?
By "out of the box," I mean in the hands of naïve users that do not upgrade the OS, choose different kernels, or change the system configuration from the default in any significant way.
Best Answer
EDIT: Based on the comments on the question and this answer, I think the link Mac OS X v10.6: Macs that use the 64-bit kernel is much more relevant.
Basically, only the mid 2010 Mac Pro, the early 2011 MacBook Pro and the mid 2011 iMac were booting by default on 64-bit mode with Snow Leopard. Since Lion (mid 2011) every new Mac is 64-bit only.
So to answer your question:
==> 2011
EDIT 2: As Vebjorn Ljosa mentioned in the comments, having the kernel run in 32-bit or 64-bit mode makes little difference for your binary, so you can probably assume that Macs sold after mid 2007 will run a 64-bit app (based on the data just below).
So it seems the last Mac to sell with a 32 bits only processor was the late 2006 Mac mini.