I take the Capitol Limited(Chicago <-> DC) most of the time when I go back to home.
Pros:
+ Comfort. You basically get a first class seat with cafeteria access. You can also purchase a whole room, but is less affordable than a plane ticket if you're traveling alone.
+ Regularity. The train leaves at the same time everyday both from DC and Chicago.
+ It reaches parts of the country not easily accessed by an Airport. If you need to visit someone in middle of nowhere USA, Amtrak might just be a better option.
+ Price. Book it in advance and you'll be saving ~$200 in airfare.
+ No TSA to check your luggage, some trains allow you to bring your bike, and there's always plenty overhead space.
+ Easy access to outlets for charging devices.
Cons:
+ Long! Chicago to DC takes 17 hours. Chicago to San Francisco can take two days. SW Pennsylvania is snaking route that feels like forever. It's really a question of how much you value your time.
+ No WIFI on most trains, so bring a book if you cannot scrum up a hotspot.