If you want an acceptable experience in most games then 4GB is okay. If you want a near perfect experience in all games but not with much/any multitasking then 8GB RAM.
If you want to do heavy multitasking then at least 16GB RAM.
With RAM being so cheap, going for less than 8GB RAM makes no sense at all.
But with a Core 2 Duo you probably won't get a smooth experience with anything higher than low-med settings, so 4GB RAM is plenty for you.
Talk about misinformation. Google for tests review sites have done where they test bottlenecks. System RAM is not a bottleneck for 99% of games. I've seen even 2GB vs 4GB tests come up as a draw so 3GB is just another GB of insurance. Examples:
http://www.legitreviews.com/article/709/3/ <- Compares 2GB to 4GB. Yes, a paltry 2GB, much of which was no doubt being used by the OS. Let's say 1GB was taken up by the OS and a few programs running in the background like a web browser and IM program or whatever. That means 2GB = 1GB free for games, and 4GB = 3GB free for games. Yet that tripling in memory barely moved the needle for most games, and even in Crysis it only added 8%. Granted, minimum fps might improve for certain games like Crysis (see:
http://www.bit-tech.net/hardware/memory/2008/07/08/is-more-memory-better/5 ) but a single number alone doesn't say much... was it just one spike or does it keep spiking down? A graph of fps over time would answer that, but unfortunately bit-tech did not provide one. The bottom line though is that 4GB is enough for almost every PC game out there, and even 3GB looks like it'd be enough, given that 2GB of system RAM already does surprisingly well for most games.
As OP stated correctly, I did say that all bets are off if you have many memory-hogging programs running in the background. But it's not that hard to close programs prior to starting one of the heavy-hitter games or mods.
Furthermore, DDR2 is a dead technology. I can't believe the kneejerk reactions in this thread telling him to get RAM because it's so cheap. It's not so cheap as to throw money away on dead technology, and for minimal gains.
I don't know what you're thinking when you diss the E8400, even at stock. I ran a stock E8400 with various cards including the HD4670, 5830, and 5850. With the HD5850 (especially with a healthy overclock) it could even comfortably play Crysis on High, albeit with low or no MSAA. OP's 7750 when overclocked is roughly the same as a stock HD5830, and he will have zero problems playing most games on High with low or no MSAA. Tougher games like Crysis, BF3, etc. will necessitate lowering settings some, but your wild claims about the crappiness of his system are unfounded, particularly when you don't even know what resolution he's running.
Thankfully others in this thread have given better and more realistic advice about how little improvement you'd get from extra system RAM.
OP would do better by sinking no more money in dead technology and saving it for a true upgrade in the future, with a totally new mobo, CPU, DDR3 RAM, etc.