I don't know your budget, so I threw together several builds for you:
Depending on the video editing software you use, Nvidia or AMD may be a better choice. If you are going to be using software that supports OpenCL (such as Sony Vegas), then you can get either, but I would recommend AMD cards. Your best options would be dual 7950s or dual 7970s. I would recommend dual 7970 6GBs, but they are very overpriced; you can get 2x 7950s for the price of a single 7970 6GB.
- Intel 3820 (quad core), 16GB 1866 memory, 256GB SSD, 2TB HDD, 7970 6GB
- Intel 3820 (quad core), 16GB 1866 memory, 256GB SSD, 2TB HDD, dual 7970 3GB
- Intel 3820 (quad core), 16GB 1866 memory, 256GB SSD, 2TB HDD, dual 7950 3GB
Now, all of these are the same, except for the GPU. The best choice, out of the 3, is the dual 7970 build, but dual 7950s would also be a fantastic choice. 2TB of mass-storage should be enough for video-editing; I have the exact HDD and it works fantastically. With that massive air-cooler (CPU), you could easily hit 4.6 to 5.0gHz with safe temperatures. Even though the 3820 is only 'partially-unlocked,' you can still overclock past the 43x multiplier (4.3gHz). It is quite easy; there are plenty of tutorials to show you how; just Google "overclocking 3820 to 5.0gHz."
AMD is a bad choice for multi-GPU options; even the 8350, the top-of-the-line AMD AM3+ CPU, will cause bottlenecking with 2-way, 3-way, or 4-way SLI/CF sollutions. I don't recommend AMD if you want to use multiple GPUs, which will help with video-editing.
If the software you are using is CUDA based (Adobe), I recommend using GTX 670s. I personally bought a 4GB 680 for gaming/Photoshop, and I love it to death, but I should have gotten dual-7950s or dual 670s for the money. Most Adobe software supports OpenCL, so using AMD GPUs would still give you fantastic performance out of the software, but some software only supports CUDA. Research the software you are/will be using; it will determine your hardware choices.
Here are the Nvidia options I came up with:
The 680 is a gread card, but it isn't worth the extra money. Any one of these builds would be fantastic. If you need to save money, look into getting an AMD 8350, but only a single GPU. The LGA 2011 CPUs are the best for multi-GPU situations, but LGA 1155 works great, as well. With Socket 2011, you have a solid upgrade path to hex-cores, such as the 3930k, and the possible octa-core Ivy Bridge-E CPUs. LGA 1155 has no upgrade after the 3770k; you are stuck with it, as far as that CPU/motherboard goes.