For video, having more ram can make a huge difference in the performance of your system. In editing, you often have to work with multiple video streams, the more ram you have the more streams you'll be able to work with in real time (with added effects, etc.).
If you are doing motion graphics, compositing, etc. then your demands will be even higher. While you are working, your graphics card will do most of the heavy lifting, but as soon as you want to have a preview you need to render, which means that you have to load each finished frame into your ram.
For example, if you are working at standard definition and your frame size is 720x480 pixels at 24bit (RGB plus alpha), at 30 frames per second for 15 seconds that's already over 3GB of ram just for playback.
So more ram equals more options and faster workflow.
Even photo is becoming crazy demanding these days.
I shot Toronto's fashion week in March. 23 shows, over 10,000 photos. All in raw format. I use Apple's Aperture for photo management and it'll tax your system like crazy once you start browsing all the photos. Don't even want to talk about the new HDR craze.