System Memory (RAM) - You should have at least 512MB of RAM in your computer in order to even think about editing video. 1GB will give you even better performance, though more than 2GB won't make a real difference for normal home video editing.

Video Capture Card or Firewire Card - If you plan to capture analog video into your computer, you'll need an analog capture card. If you have a digital camcorder, you can use a less expensive firewire card for your video capture tasks.

One note: you don't need a 3D card with a lot of memory - video is 2D and doesn't need the same graphics engine needed for gaming. Spend your money on boosting system memory instead. However, cards like the ATI All-in-Wonder will provide both video capture capability as well as excellent 3D performance in one package.

A Large and Fast Hard Drive - In addition to your system drive, you'll want a second drive for video capture and storage. Get a large drive (at least 120GB) and something that runs at 7200RPM or faster. An internal drive is best, but an external firewire drive will work if you want something portable. Avoid USB drives as even USB2 drives don't have the sustained transfer speeds needed for playing video (especially if you have several USB devices already connected to your system).

Video Editing Software - Without editing software, all the hardware in the world won't do you any good. There are many excellent programs out there for around $100 as well as several semi-professional programs for a higher price.