From Amtrak.com, select Deals and choose Advertised Specials. There you'll find a number of route/city specific discounts.
There are also many discounts (promotion codes, etc.) not advertised on Amtrak's website. You can find a pretty complete list at:
http://www.railserve.com/amtrak_coupons.html
For example, there's currently a 20% off discount for most routes in the Midwest.