MacPro 2008
OS 10.6.8

I'm afraid I have no solution, but I can confirm that the issue is not unique -- it's ongoing here -- and add a little more info. I've pretty much given up, myself, and plan to solve the problem by biting the hardware bullet and springing for the new MacPro, but I'll go ahead and describe my own experience. I've included what I believe is the relevant Software Update listing below.

So, for what it's worth:

Start-ups, when successful, require multiple attempts, during which the system continuously tries to reboot itself (after a few discouraging clicks) until shut down with the power button. After incrementally testing peripherals, including shutting off my external speakers, I eventually even detached the USB connecter that lets me use my Wacom Cintiq 22 as a tablet, instead of just a monitor. Wacom tablets have always been somewhat problematic (most notably interfering with sleep mode). I tried starting up once with the Tablet, itself, actually turned off, but, strangely, I was unable to turn it back on till I shut back down. In these current straits, the MacPro will not wake at all, if allowed to sleep.

It may be worth noting that the problem gets progressively worse over time. Lately this has included spontaneous restarts within the first half hour or so of an actually successful boot (during which internet apps are particularly slow to load and the finder is extremely sluggish). If I spend that time elsewhere and leave it alone, it seems to run normally thereafter, but I've only tried that a few times so far. It generally won't even finish booting up in safe mode, where it quits halfway through the gray apple screen progress bar. Oddly enough, tonight I started it up in Target Disk Mode, then forgot to eject it from the desktop before powering down and disconnecting it. Immediately after that, it booted up perfectly, and has been patiently awaiting my attention for over an hour.

I have had problems like this before the last update, and suspected they were related to, or at least exacerbated, by Photoshop and an aging graphics card. I'm still not sure that isn't the case, perhaps with Wacom conflict in the mix. On my first trip to the repair shop, we replaced a defective secondary internal disk. More recently, the technician found nothing wrong at all, and upon return everything did, indeed, seem to be running smoothly (which might seem to implicate the Cintiq). The problems returned with a vengeance, however, after my last software update.

I'm extraordinarily slow about installing the recommended items (because I'm usually deep into PShop when the messages arrive), so the following -- most of which of which were released last fall -- may well be the same ones that plagued the original sponsor of this query:

Remote Desktop Client Update 3.5.4
Security Update 2013-004 1.0
iTunes 11.1.5
Migration Assistant Update for Snow 1.1
Java for Mac OS X 10.6 Update 17 17.0

None of this seems particularly revealing, but maybe it will be helpful to someone.