Durante cast his critical eye over the Dark Souls 3 PC port and found it to be the best in the series. That hasn't stopped an infuriating crash bug creeping in though. Players approaching the Firelink Shrine bonfire are crashing to desktop, again and again, until they go hollow. I know the pain, because I came up against the same bug and had to cobble together a fix to progress—hopefully it'll work for you.
As far as I can tell—and there's some speculation involved—the graphics drivers hit an issue when a bonfire's lighting meets From's beautiful flowing cloth. I'm using a GeForce 780Ti on drivers 364.72 and the crashes happen at Firelink, the High Wall and at the Cliffside bonfire in the Undead Settlement, but only when I'm wearing the clothy carb of a caster or flamboyant swordsman. Something with dangly bits, basically.
Setting your lighting to low (which makes minimal difference to the overall look) stops the crashes, albeit with a nerve-wracking hitch every so often. However, Dark Souls 3 doesn't currently remember this setting, so every time you restart the game, you need to reapply the change.
From Software ought to be thoroughly aware of the problem by now, so I've got my fingers crossed for a driver update in the near future. The issue does ease in later locations.