Amtrak

Amtrak offers a series of USA Rail Passes; as of October 2015 they are

8 segments within 15 days $459

12 segments within 30 days $689

18 segments within 45 days $899

To discourage commuters from buying a pass (as opposed to a multi-ride ticket), travel is restricted to four one-way trips between any two cities and the cities in between them on the same route.

As with rail passes in most countries, these are for basic travel in coach class, so additional accommodations (e.g. sleeping compartments, business class) will cost extra. Also, the passes cannot be used on the Acela Express or Auto Train, or segments operated by some Thruway buses or VIA Rail Canada.

Two important caveats:

The pass functions more like a coupon book than a pass. It does not get you actual passage on a train; instead, you must make reservations with it and pick up your tickets beforehand. You can make arrangements with a ticket agent at station, or make reservations over the phone and use your reservation number to pick up the ticket from any QuikTrak machine.

The number of seats available for pass redemption are limited, so you will need to make reservations early, possibly weeks in advance depending on the route, if you don't want to pay a surcharge. I believe blackout dates will also apply around major public holidays.

Greyhound

Greyhound used to offer a Discovery Pass, but this has been discontinued. The official replacement is to book individual tickets in advance, which is not really a replacement:

Is there a similar type of ticket option I’ll be able to choose going forward? Advance purchase fares on greyhound.com and greyhound.ca provide excellent value compared with the Discovery Pass. The traveler is provided accurate schedule information for Greyhound and other bus companies, and depending on the schedule, can also select an Express route, which offers exciting amenities and the security of a guaranteed seat.

The downside is that "Going Greyhound" is not a byword for a speedy, high quality travel experience, though all the buses I have taken have been safe, air-conditioned, and relatively clean. I cannot say the same, of course, for many city bus terminals.