In approximate order of first setting foot on the train:
Coast Starlight (entire route)
Empire Builder (both legs, entire route)
Pacific Surfliner (entire route)
San Joaquins (Bakersfield to Sacramento)
Acela Express (entire route)
California Zephyr (Denver to Salt Lake City)
Crescent (Charlotte to Washington, DC)
Cardinal (entire route)
Capitol Limited (entire route)
Northeast Regional (Washington, DC to Boston)
Cascades (Seattle to Portland)
Lake Shore Limited (New York Penn to Chicago)
Texas Eagle (Chicago to St. Louis, Fall 2010 detour route only)
Missouri River Runner (entire route)
Southwest Chief (Kansas City to Los Angeles)
Adirondack (New York Penn to Plattsburgh)
Also, off-topic but:
DB RE (Rosenhiem to München)
TGV (LGV Sud-Ouest, Paris to Poitiers)
DB ICE line 42 (München to Frankfurt (Main) Flughafen)
TGV (LGV Sud-Est, Paris to Dijon)
SNCF TER (Beaune to Dijon)
Finland VR Sibelius (Helsinki to St. Petersburg)
Alaska Railroad (entire route)
CountryLink North Coast (Sydney to Casino)
Queensland Rail Sunlander (Brisbane to Cairns)