By default, even on fully 64-bit Macs, Snow Leopard boots into a 32-bit kernel. This is because not all kernel extensions are 64-bit ready. This short HOW-TO explains how to tell which mode you've booted into.
With the introduction of Snow Leopard, there is a some confusion about 32/64-bit apps and 32/64-bit Extensible Firmware Interface (EFI) and 32/64-bit kernel extensions. We'll be sorting all that out in the coming weeks, piece by piece, to make it understandable.
Apple knows best on this. By default, your Snow Leopard system (except for Xserves) boots into a 32-bit kernel, even on the latest Macs. That doesn't keep you from running 64-bit applications and addressing more than 2 GB of RAM.
The problem is that you may have some kernel extensions that are not 64-bit capable. You can try booting into the 64-bit kernel by holding down the 6 and 4 keys together at boot, but not everything may work correctly. To get a feel for some extensions that would be a problem, take a look at: About This Mac -> More Info -> Software -> Extensions. On my system, several are still flagged as 32-bit only.
System profiler shows whether kernel extensions are 64-bit
For now, you may be wondering how to tell if your system was booted into 32 or 64-bit kernel mode. Just take the same route above, but stop at Software, and look for the "64-bit Kernel and Extensions" flag, circled in red below.
System profiler shows mode booted into
There's really no stigma attached to running in the 32-bit kernel mode, and, in time, all our kernel extensions will be 64-bit. It's just one more step in the roadmap to a full 64-bit Mac.