First off, thanks for all the good info folks. I'm flying into DUS in a few weeks with a Eurail pass and had no idea if the Skytrain was included. Now I know it isn't!
I have a follow-up question. I'm going straight to Cologne from DUS. Since the rail pass is good on the S-bahn, per your info, I would like to take the S11 into Düsseldorf and connect from there. But I'll need to activate the pass first. Does the S-bahn station in the airport have a manned ticket counter somewhere where I could probably do this? Backup plan is to pay the Skytrain fare and activate the pass at the Düsseldorf Flughafen.