Amtrak's California Zephyr line drops passengers at Green River, Utah, which is about 50 miles north of Moab. From there, you can arrange a shuttle with one of Moab's in-town transportation outfits (see listings at: http://www.moabadventurecenter.com/transportation/shuttle.php). You could also potentially fly into Canyonlands Field Airport on the western side of Arches National Park with US Airways, though fares to this small airport will probably be more expensive than just renting a car out of somewhere like Grand Junction, CO, or even Salt Lake City.