It was once the case that graphics card RAM wasn't super important -- as long as you had one or two gigabytes of dedicated video memory, you'd be right for most games. The last few days however have utterly wrecked this rule-of-thumb, first with Bethesda's The Evil Within recommending 4GB and now Shadow of Mordor requesting a massive 6GB for its ultra setting.
Ultra? Pfft, why not just run it at high and be done with it? Well, that's not going to do you much good, as that setting needs a healthy 3GB. No, the vast majority of consumer graphics cards on the market today will only be able to handle Shadow of Mordor's medium texture level, which needs a comparatively paltry 2GB. All these assume you're running at a resolution of 1920 x 1080.
This information is courtesy of a NeoGAF user called "Regret Truth", who provided the above screenshot of the game's video options. Note that the ultra setting requires the "Ultra HD Texture Pack" in order to work and sounds very much like a separate download.
Now, something to keep in mind is that you'll be able to run the higher settings even if your graphics card doesn't have the required memory. Instead, your system RAM will be used instead, though this is much slower for the GPU to access. If you don't have the physical sticks available, then it'll hit the pagefile and that's when you're really in trouble... unless you enjoy punishing every data bus in your PC.
Image: Regret Truth / NeoGAF