Please note that I do all editing of standard-definition video; I have (unfortunately) no experience editing HD video.
From my experience working with digital video, it's at least as important to have a good video capture card (NOTE: Not graphics card, in the sense of a GeForce or Radeon card) as a fast CPU on an editing machine.
Here's a good real-life comparison:
At my school, I use a purpose-built video editing station, complete with the works; breakout box, external TV monitor, etc. The computer itself isn't very impressive; it has a 2.66 GHz P4, 512MB RAM, multiple hard drives, and a GeForce 5600 AGP grahpics card.
For video editing at home, I use my computer; a 2.2GHz Athlon 64, 1GB RAM, X600 PCIe card (I don't play many games...), and a 250GB HDD.
Hardware-wise, my personal machine blows the school's editing station out of the water, but the machine at school is considerably faster at editing video. My machine becomes sluggish when I start adding multiple video effects, whereas the station at school continues, unflustered. The difference becomes even more pronounced when encoding the final video to MPEG.
How could it be? That, my friend, is the magic of the VIDEO CAPTURE CARD! The video capture card does realtime processing of all the video effects, filters, etc. and also does hardware-accelerated MPEG rendering.
Essentially, the video capture card is optimized for displaying, editing, and encoding video. It's specialized for one specific task, whereas CPU rendering utilizes the CPU, which is not optimized for video, and which is already doing a multitude of other things.
Unfortunately, I don't know a great deal about the video capture cards themselves; all I know is that Matrox makes some very high-end video editing solutions, and that PNY makes "Professional Video Editions" of nVidia Quadro graphics cards, which come with breakout boxes.
Pretty much any quad-core CPU with lots of RAM (at least 2 GB; I'd go for 4) will do the job, as long as you pair it with a dedicated video processing card.
Finally, you'll want a lot of hard drive space, a lot of RAM, and dual displays.