How old are Macs that cannot run 64-bit applications?
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:


  In what year were the last Macs that were not capable (without user tweaking) of running 64-bit software sold?


==> 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).




Mac mini:


last 32-bit only processors: late 2006
oldest 64-bit capable processors: mid 2007

iMac:


last 32-bit only processors: early 2006
oldest 64-bit capable processors: late 2006

Mac Pro:


always been 64-bit capable

MacBook:


last 32-bit only processors: early 2006
oldest 64-bit capable processors: late 2006

MacBook Pro:


last 32-bit only processors: early 2006
oldest 64-bit capable processors: late 2006

MacBook Air:


always been 64-bit capable



So it seems the last Mac to sell with a 32 bits only processor was the late 2006 Mac mini.