In the past, I've run just one day a week, 20-30 minutes max. I talked to a friend who was a collegiate runner and he suggested that the terrain should match what you would see in your 'cross races. So I run on grass and dirt primarily. And I mix in short, steep little hills, sandy patches and some tight, twisty singletrack.
Last year I did more running than I needed to. I could crush people during the run-ups, but only 3 of my races actually had a run-up in them. This year, the running will taper off once the actual racing season starts.
Yes, I run. Once or twice a week. Not necc. as part of 'cross, but because I'm a field service guy who's just trying to keep my fitness up. Sometimes I get to a hotel after 7pm, and I'm tired, hungry and don't know the neighborhood. I've been able to develop a decent running motor (Saturday I did a 5K for fun and clocked a 23:08, my first ever foot race). Now I'll need to start adding some sprints in.