A few people have been asking about rebuilding PCs for Battlefield 3, so I've posted an incredibly basic guide below.
IMPORTANT: If you have never built a PC then this is probably not the time. If you want to try (and it is actually fairly easy) then there's a guide here.
For most people, however, I would definitely suggest getting a custom desktop PC build from somewhere like here in the UK or here in the US. (I am really not sure where to recommend for North America, so I am just going on recommendations from internet chums.) For PC Specialist in the UK I know stacks of people who have made purchases and been quite happy, so I am comfortable recommending that. Basically look at the specs below and order your PC accordingly.
Here are the recommend tech specs for the game:
OS: Windows 7 64-bit
Processor: Quad-core Intel or AMD CPU
Graphics card: DirectX 11 Nvidia or AMD ATI card, Nvidia GeForce GTX 560 or ATI Radeon 6950.
Graphics card memory: 1 GB
Sound card: DirectX compatibl sound card
Hard drive: 15 GB for disc version or 10 GB for digital version
1. The most important thing is probably your graphics card.
The one I am going to recommend is Nvidia's 560 Ti. We just seem to be getting less issues than with ATi cards, and the Ti version of the 560 is pretty hefty in all regards, which will mean that the real sweet spot for clever graphical features is more obtainable. They're about $220 or £170, I think.
2. The other performance bottleneck is likely to be your CPU. This is a more complicated issue, because upgrading a CPU will probably mean you need a new motherboard and memory.
Basically the CPU to go for is the Intel i5 2500k. It's relatively cheap at just over $200, and can be rapidly overclocked in the bios for a bit of extra kick. The issue is, of course, that you will need a socket 1155 motherboard. If you aren't already on an i5 or better than chances are you won't have a motherboard that supports it, and that's a whole other kettle of upgrades. I am not going to go into that here, suffice to say that I am extremely pleased with my full system upgrade based on these sorts of specs, and Battlefield 3 looks pretty good on it.
3. All this is moot if you monitor is nob, like mine.
I am probably going to upgrade to an Iiyama like this one.
4. If you have money to spare then getting an SSD is essential.
I cannot stress how useful making your C: an SSD with Windows and some important apps on it is. You will still need a big fat normal HD to store everything else on, but no single upgrade will improve your general computer-using experience more than this. Not relevant to Battlefield, perhaps, but worth stating.