What is better - 12x1 Gb RAM vs 3x4 Gb RAM? Does having more DIMMs in parallel faster, like adding more disks to a RAID-0 array?
This doesn't make a lot of sense.
There's an optimum point between number of sticks of RAM used and size of the sticks, a balancing point between cost (lower capacity costs less), expansion (using larger capacity sticks leaves slots free to expand memory without throwing away the money you've already spent on memory) and reliability (less to do with some kind of "RAID" idea, more to do with the chances of something failing and the impact if it does fail). There's also the issue of what memory configuration works best for the motherboard and CPU you're using (e.g. triple channel memory vs. dual channel).
There are some technologies out there that allow you to have "backup" memory in case the memory you're using fails, but unless you're going for very high availability indeed then I'm not sure it's worth it. In either case, its not helpful to think of this tech in terms of "RAID for memory", it needs to be considered in its own light.
Meaningless question without ram clock speed/ front side bus numbers. Extra meaningless because the "R" in raid is for "redundancy" and there is no need for redundancy in volatile memory.
Pick the one that's faster.
It Depends. Consult the documentation for your motherboard. Often it is the case that DIMMs should be installed in matched pairs rather than odd numbers.
I'm going out on a limb here and saying it's safe to assume it's triple channel, since both configs he asked about are divisible by 3. He's asking if four sets of 3Gb (3x1Gb) RAM is faster than a single package of 12Gb (3x4Gb) RAM. And he's referencing RAID with the same thinking of of a RAID 0 set where more parallel channels equals faster read-write, more accurately though like the difference between single and multi core processing.
So, You already read your manual and know about channel groups, the question still applies. But since no one on this forum was able to make that jump in communication, and a site i found for audio editing said there was no advantage (albeit that's far less demanding than server or film/3D work), I'm going to assume the same thing. Saves me money on cooling (workstation stuff, 3D, I overclock but not overly), and allows me to buy more if I need to like one of the fellows said.