I just got a Mac and I have Snow Leopard installed. I checked my arch type and it says i386.
How is it possible? 10.6 is 64-bit, right?
By default Mac OS X still starts up using a 32-bit kernel. If your computer supports the 64-bit kernel, and you start up using the 64-bit kernel it will display x86_64 instead of i386.
You can find out more about the use of the 32-bit kernel by default in the Why does my Mac OS X 10.6 kernel run in 32-bit mode? question here on Super User.