Firstly, I'd like to thank those of you who've posted possible solutions to this problem. I've been getting BSOD's and crashes/freezes since launch, and am nearly at my wits end trying to troubleshoot the issue (16+ hours into trying to fix this). Here's what I've tried so far, per suggestions on this thread:
1. Updated video drive, audio drive, Logitech drive, PhysX drive, and every other drive I could find
2. Set program to run as admin
3. Ran a mdsched command to check memory (RAM is fine)
4. Used msconfig to par down to the bare minimum of programs
5. Dropped NVIDIA video drive down to 320.49, then down to the 314.22 version
6. Set PhysX to run on CPU
7. Virus/malware scans
8. Disabling app overlays like Steam

My results: Every once in a while I'll have a good day, and play for 5+ hours with no problems. Most of the time, however, I cannot stay logged in for 5 min without a blue screen or a crash. I know it's not an overheating issue because my rig has a liquid cooling system and temp alarms, which have not been triggered. Researching driver sweeper programs have yielded iffy results--some people seem to swear by them, others claim they are completely unnecessary. I also haven't tried the most recent suggestions (switching off the in-game frame limiter and defragging the folder), so those will be my next attempts, followed by a driver sweep if that fails.

Just wanted to report what is/is not working for me, in case it helps direct someone else to the source of their woes. And believe me when I say that I share your frustrations...I play four other games, and only FFXIV seems to have this problem, despite the strong indication that it's an issue with the rig and not SE. All the other games are rather graphically-demanding, so I couldn't say why those programs are fine and FFXIV is not.