Cyclists who want to take their bicycles aboard Amtrak trains without dealing with a considerable amount of hassle shouldn't get their hopes up.
Of 35 named Amtrak routes only eight have roll-on service for bicycles or allow you to check unboxed bikes as baggage. Most of these routes are on the West Coast; cyclists in the rest of the country should be prepared to putz around with bicycle boxes and go out of their way to make sure they board at a station that accepts checked baggage.
If you're lucky enough to live in an area that does accept bikes, you'll still need to call ahead to reserve a space, be prepared to pay extra fees, and keep recumbent or other unusual bikes at home. If you're trying to take a bike on a route that doesn't have roll-on bicycle policy you might still manage to get one aboard by calling 1-800-USA-RAIL.
Though Amtrak, a government-managed corporation, deserves credit for taking some steps to accommodate cyclists, it's overall failure to court a group that would otherwise be some its most loyal riders represents a lapse in managerial judgment.
Though Amtrak has seen a slight boost in ridership during recent years, as seen in the graph below, ridership numbers have been declining in recent months and overall the number of people who use the service remains embarrassingly small.

According to a Congressional Budget Office Report, Amtrak served a scant 2.3 percent of domestic intercity passengers traveling by commercial carrier in 2000. The railroad carried 23 million passengers in 2000, compared with 611 million passengers on commercial airlines (61.2 percent of the total) and 365 million on intercity buses (36.5 percent of the total).
Likewise, according to the same report: "The railroad's 5.5 billion passenger-miles in 2000 pale in comparison with the 516.1 billion traveled on airlines (92.2 percent of total intercity passenger-miles on commercial carriers) and the 37.9 billion traveled on buses (6.8 percent of the total). Travel by private automobile reigned supreme, however, accounting for more than 2.5 trillion passenger-miles in 2000.
Catering to cyclists (many of whom are considerably less tied to their cars than most Americans and willing to use public transportation) is one easy way to get those numbers to start rising again.