What options do I have for scenic long-distance train journeys in North America that last for 2 nights or more?

Coast Starlight is a good option in the US, without a doubt. Southwest Chief should be good too. Both start from Los Angeles Union Station (on one end, Starlight goes to/from Seattle, the Chief goes to/from Chicago). If you heard about US trains with viewing cars - that's these two.

Never took either of them myself, but heard very good things... If only I had the time and the means!

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How could I forget? California Zephyr, of course, one of the most famous! This one goes from Chicago to San Francisco (Emeryville, then bus across the bay).

The Canadian runs from Toronto to Vancouver, taking a bit over three days. On the way you'll stop in many of Canada's major cities, and get to travel through some of the most spectacular scenery in the world, including The Rockies. You can also do subsections of that trip if you don't have three-plus days. A number of the Edmonton-Vancouver routes area particularly impressive.

If you prefer the East, you can do Montreal-Halifax, which takes just under 24 hours along the St Lawrence. For the total Canadian experience combine the two.

I took the Coast Starlight from Seattle to Los Angeles once and while there is always something to see outside, I wouldn't call it very scenic for most of the journey. The stretch in central California around San Luis Obispo was quite scenic with nice rolling hills. You also go through Vandenberg Air Force base with its rocket lunch pads, an area which can not be visited by car, but that's only 20 minutes or so.

I assume any train that goes over the Rockies is much more scenic.

Also, the coast Starlight leaves Seattle at 9:45 am and arrives in LA at 9 pm the next day, giving you only one night on the train (not two as requested).