I fear some articles on this website goes to waste on some people. Just do a search.
Rise of the Tomb Raider
Shadows of Mordor
GTA V
There might be other titles that also use more, however, these are the games I am interested in and have noticed use a lot of VRAM.
With DX12 games coming out, I am sure we will see even more VRAM used in the near future. Games like Deus Ex - Mankind Divided and so forth.
Then there is the modding community, for games, which add extra details to textures, more objects, more landscapes. I am sure when Fallout 4's Creation Kits comes out, that will also go over the 6GB VRAM usage for some of us.
Things like Anti-Aliasing and Resolution also comes into play for people like me that don't like jaggies. Downside? More VRAM usage.
Then there are all the monitors with their refresh rates... 60hz, 75hz 85Hz 100Hz 120Hz 144Hz+ I prefer mine stable at 120FPS if you run out of VRAM, you can be sure to see those numbers dip more often than you like... loosely translated... in-game stuttering.
And last but not least. It's always a good thing to have that little extra head room when it comes to VRAM to make things a little future proof, especially when you are someone like me that doesn't enjoy upgrading his GPU once a year and being wallet raped while doing it.
Many factors are involved, more than people would like to realize.
The performance impact translates into what people refer to as "Stuttering" this happens when new textures have to be loaded into the VRAM and older textures have to be removed. When there is enough VRAM headroom for all the textures, then there is no problem, especially when you have to move back and forth to prior locations within the game world.
Note: there are other components that will also have to work in harmony and conjunction with each other for everything to work smoothly. For example, a PC using a SSD won't struggle as much vs one that still uses an HDD.
Often referred to as a bottleneck.