There are marvelous train systems throughout the world, even a few in North America. In the USA and Canada, consult Amtrak or Via Rail for some of their long-distance service. In the USA, there are excellent trains running up and down the West Coast (the Coast Starlight for one), with fine sleeping accommodations, good coach cars, reasonably priced dining cars, observation lounge cars, and the like. Similar trains operate from the East Coast to the West, such as the California Zephyr through Chicago and Denver to San Francisco, the Southwest Chief from Chicago through Kansas City and New Mexico to Los Angeles, and the Sunshine Limited, from Miami through New Orleans to Los Angeles. If you entrain in the northeast, you still have to change trains in Chicago, 50 years after a rail expert complained that "a pig can travel in one car coast to coast, but people can't." Still, trains out of New York, Boston and Washington such as the Capitol Limited or the Lake Shore Limited are fun to ride, though slower than their western counterparts, and not equipped with double-decker observation cars (all those ancient tunnels to go through, you see).
Phone Amtrak at 800/USA RAIL or go online (www.amtrak.com) for further information. For Via Rail Canada fares and information call 888/VIA RAIL or go online (www.viarail.ca). Note that you will need Government-issued photo ID to get ticketed or to board the train now.