I biked to Seattle from Michigan, then took the Amtrak Empire Builder back to Chicago, where I was picked up. Putting the bike on the train was EXTREMELY easy, I walked up, paid $10 for the bike box (which jamawani describes), took of my pedals, turned my handlebars, and was good to go. No special tools or an expensive bike box were needed.
I enjoyed the extra time on the train to see scenery and talk to people. Baggage wasn't a concern -- I had been traveling light for several months already! Amtrak + bike touring = highly recommended.