The Vancouver, BC to Eugene, Oregon runs gains free Wi-Fi: How do you get people to choose the train over a plane or car? You make it comfortable, fast, reliable, and useful. Amtrak has long advertised the notion of getting work done, and on some of the Cascades run (from Vancouver through Seattle and Portland down to Eugene) you can get a business-class seat with a power outlet. Now, a Wi-Fi plan long in the testing is available and at no cost.
Amtrak provides Wi-Fi service on the Northeast Acela run, and many regional train operations also offer Internet access. Over 800,000 passengers rode part or all of the Cascades line during 2010, the high-water mark for ridership. I have a trip planned to Portland in February, and might opt for train over car because of the Wi-Fi.
Service is free for now, and may remain free; it depends on usage and other factors. Internet service is typically installed to provide operational service for the train line, as well as passenger access, but it's unclear on whether this is just an amenity.