Generally speaking, if you are running a 64-bit native OS and a 64-bit native game, then yes, it can help. At the very least more RAM means less paging (reading and writing less used sections of memory to disk to free up RAM), and less paging means a faster computer overall. Generally 8GB would be enough so that most games won't compete with the OS for memory and allow for processes to run smoother because again, less paging.
In game specific terms, you can have more/bigger textures in memory as well as more of a level and characters loaded as well, but only if the game is written in such a way as to take advantage of the bigger memory pool. This really only applies to games with dynamic limits.
###TL;DR Its only an advantage if the game is written to take advantage of it: Games who's only limitation is the size of available memory are generally the only ones to see a performance boost by more than 4GB of RAM.