If you are playing games that are heavy on the GPU, then you need to invest in a beefy graphics card. If 4K gaming is your thing, no less than a graphics card with 12GB of graphics memory is enough. Modern games demand cards with at least 4GB memory, while 6GB or more is ideal for high-end 1080p gameplay. If you want to play games at 1080p and on high graphics settings, then your prospective GPU should feature 8GB of memory.
In general, most games these days require 4-8GB of GPU RAM in order to function correctly. When running a game or piece of software that has lots of graphics, the GPU RAM will fill up fast. If you do not have enough graphics RAM to keep your apps running, they cannot load the resources that they need. The more pixels that have to render per frame, the harder it is on your GPU.
Depending on what kind of games you are playing, throwing more VRAM into your graphics card does not mean that your GPU is going to do any better. Some games are not optimized well, meaning that you have to fiddle around with graphics settings in order to achieve decent performance, and if you have ever modded a game such as Skyrim, then you will probably see graphics mods saying you need a GPU with lots of VRAM. GPU power tends to translate into price, so it is not necessarily worth buying a gaming-specific graphics card unless you are interested in running games on their highest settings, and want the best possible performance for your dollars. If you are looking to build a high-end computer for competitive gaming, and need a monitor with high refresh rates in order to get the edge over the competition, then you are probably going to want to buy a high-end graphics card capable of accommodating high refresh rates.
Speaking of monitor resolution, if you are on the market for a new graphics processor, you will also want to take into account what your monitors (or one you are planning on purchasing) refresh rates are. The key is, if you are planning to play games competitively at 1080p, be sure you get the cards speed rating on the games you intend on playing on a 1, because the last thing you would want is to wind up with an expensive monitor that does not have a powerful enough GPU to adequately support it. Only the latest AAA titles running everything turned to Ultra at 4K require anywhere near this amount of VRAM, and even then, you will want a super-high-end card, so making sure your GPU is up-to-date and is of a quality that you will need, and that you can afford, is more important than worrying about VRAM.
Well, we already mentioned that most recent graphics cards ship with 8GB VRAM, so this is certainly something you should strive for if you want a GPU with the best possible future-proofing, or if you are planning to buy a 1440p display right away. Most games running at 1080p will be comfortable using a 6GB graphics card with GDDR5 or higher vram. Installing a graphics card with at least 6GB of GDDR6 VRAM is likely to get you through most graphics-based tasks and games.