Well most of Amtrak's trains are reserved, but that doesn't mean you can't buy a ticket on board, some people do. But, Amtrak has changed its policies in recent years (especially with the advent of e-ticketing) to encourage people to buy before they board. You will pay the highest fare possible on board, so there is no incentive to not do the reservation. However, you must pay for your reservation before you board as well. The days of making a reservation, and then paying that price on board are gone on most routes. As stated on Amtrak.com...
Onboard
On most Amtrak trains, only the full, undiscounted, unrestricted fare will be available for purchase onboard the train. This is regardless of reservations made or fares previously quoted. To secure the best available fare, passengers should purchase tickets prior to boarding the trains.