The CPU handles everything (Variables such as health, which 3D model is where, what happens when you press the UP key, etc.), the RAM acts as a temporary high-speed storage device (Transferring 1GB of data from a hard drive to a hard drive will take around 10-15 minutes. From a hard drive to RAM, however, it will only take a few seconds, if not milliseconds.)
At the moment, most games and game engines are offloading the GPU's work with the CPU (like Skyrim's particles and shadows. Normally done by the GPU, but since a console's GPU is slow compared to the processor, the processor takes over somewhat, albeit badly.) so an upgrade in a CPU AS WELL AS a GPU will give you a noticeable performance increase in heavily demanding games, like Crysis 2 or any *Cough* "Next gen" games.
If you were to upgrade DDR2 (Power hungry, low latency, slow(er) operating speed) 4GB ram to DDR3 (Not so power hungry (30-40%), high latency (2X DDR2's latency), fast(er) operating speed (1.5-3X faster) 4GB ram, you will either notice a slight performance boost (Think 1FPS boost in a game if your lucky), or a slight performance decrease (Think 1-3 seconds more time in small-medium file-hosting/database server) or none at all (Almost always is the case).
Ideally, 4GB of ram is what you need right now (And will always need if you want legacy support like me), but things seem to be teetering towards 64bit, so more than 4GB would be a half-good idea at future proofing your computer if you have a blazing £1000 computer that will keep up with next generation's £500 computer.
You'll only really notice the difference in performance with more ram if your upgrading from 1/2 to 2/4 GB, as the game doesn't have to use the HDD as virtual memory more than it is intended to.
The GPU is what PC games (Not console games, mind you!) need the most. A GPU is rather hard to describe, so I recommend that you Google it (Like you should have done with your question anyway). BUT! In order to see the performance gain from a lesser-performing GPU to a greater-performing GPU, you need to have a good processor that can send instructions for the GPU to do at a fast enough rate that the faster and better GPU will show a better result. Otherwise, you just have an expensive GPU performing as well as a cheap GPU.
A motherboard is what connects everything. Generally, the more you pay for a motherboard, the more stuff you can do with it (Crossfire, more HDDs, more RAM, better CPU, possibility to put a top of the line GPU in your computer and not be ever so slightly bottlenecked by an older PCI-e slot). Won't see much performance gain in gaming by just switching all your components to a different motherboard and then just going back to your normal computer escapades.