A 32-bit OS can theoreticaly address a maximum of 4GB of memory, but that includes the memory on your video card and a few other things. I've 4GB in my 32-bit Vista, and it recognizes that there's 4GB, but only lets me have 3GB to play with. 64-bit OS's can theoretically address something like 16 exabytes of RAM, but practically speaking most limit themselves to somewhere between 128 and 512GB. Which should be enough for anyone.
