Seconding the California Zephyr. The stretch between Chicago and Denver isn't much to write home about since it's just plains, but the rest of the way between Denver and Emeryville/San Francisco is absolutely stunning. The scenery just keeps coming too as it takes you through both the Rockies in Colorado and the Sierra Nevadas in Nevada and California. I've only been able to take the route once, but I'm already in line to take it again because it was just that great.

In terms of the best bit of scenery in the network though, Glacier National Park on the Empire Builder is, in my opinion, hands down the most scenic stretch on any route in the entire Amtrak network. I've actually taken the Empire Builder twice specifically because of that segment (once in summer, the other in winter). The bit after Seattle and through the Cascades in Washington is quite scenic as well. If you do this route though, be sure to do it West to East (Seattle toward Chicago), otherwise you run the risk of passing through Glacier Park after it's already dark and missing the best scenery. The Zephyr is best done East to West (Chicago toward Emeryville, CA). The Westbound train is scheduled to leave Denver into the Rockies early in the morning, so even a several-hour delay should still leave you enough time to see most, if not all, of the scenery in the Rockies. Heading East toward Chicago, the train is scheduled to arrive at Denver in the evening, so it would take a much smaller delay to cause the train to pass through the Rockies in the dark.