The Empire Builder (leaving Chicago) generally runs:
2 locos, baggage, transition sleeper, 1 or 2 Seattle sleepers (depending on time of year), dining car, regular Seattle coach, Seattle coach smoking (for the next month or so, anyway), Portland sightseer lounge, Portland coach, Portland coach baggage, Portland sleeper, St. Paul "short" coach (seasonal, may be Hi-Level car), followed by mail and express cars (boxcars, refrigerated cars, roadrailers).
If you're really nerdy and into line numbers, they are:
0710 (Dorm car)
0731 (Seattle Sleeper - seasonal)
0730 (Seattle Sleeper)
0711 (Seattle Coach)
0712 (Seattle Coach)
2714 (Portland Coach)
2715 (Portland Coach)
2730 (Portland Sleeper)
0709 (St. Paul coach - seasonal)
The Hiawathas run: Locomotive (facing north/west), four Horizon coaches (sometimes an ex-metroliner cab mixed in there), cabbage car (facing south/east, sometimes replaced with 2nd locomotive depending on availability of cabbage cars).
The Chicago-Pontiac trains generally run with a locomotive, four coaches, Horizon cafe/business class, and a cabbage (350/355 may have a different arrangement).
Coast Starlight has 2 locos, baggage, transition sleeper, 2 or 3 sleepers (depending on season), Hi-Level lounge (Pacific Parlour), Dining Car, Sightseer Lounge, 3 to 5 coaches (depending on season). The Starlight tends to run with mostly Superliner II equipment.
In the Pacific Northwest, the Cascades corridor trains use the Spanish Talgo trainsets, which have a power car, 2 business class cars, a dining car (used as a lounge car south of Seattle, and "real" diner north of Seattle), Bistro (cafe), and 7 or 8 regular Talgo coaches, then a small baggage car (I think the "Cascades" Talgos run with 7 coaches, and the "Las Vegas" one has 8, but I'm not 100% sure of that). These are sandwiched between a loco (usually F59) and a cabbage (or 2nd loco).
The green and brown Talgos run Seattle-Portland-Eugene service, and the blue and grey "Las Vegas Talgo" (which has probably never even been to Las Vegas) runs Seattle-Vancouver.
Out east, the Silver Service (and Crescent) run with locos (1 or 2), baggage, dorm, Viewliners (1 to 3 depending on train and time of year), Heritage diner, Amfleet lounge, Amfleet II coaches. This arrangement used to be found on the Cardinal as well, but now it just runs with a loco, Viewliner, dinette, coaches (no baggage car, and frequently no dorm). That is also found on the Three Rivers, except that train might have a baggage car (not sure), and usually has a few thousand express cars on the rear (though that number may have been reduced recently).
When I rode the Lake Shore last year, it ran with 2 locos, baggage, Boston coaches, lounge, diner (to New York), New York coaches, New York sleeper, dorm, baggage, express. If there had been a Boston sleeper, it would have run forward of the coaches (but it was blanked for both trips, even way back in January 2003). Now the Boston section runs as a connection in Albany, until May. The Lake Shore train matches the silver service trains now, Chicago-New York. I don't know what the Boston train looks like, but I'm guessing it's a loco, cafe, and two coaches.
A few Midwest corridor trains run with Superliners in the winter (International, and I think Illinois Zephyr), for various reasons (including the fact that two dozen Horizon coaches get sent to Florida in January for special trains).
The Heartland flyer uses 1 loco, Hi Level coach, Superliner Coach/Cafe, Hi Level Coach, and another loco.
There are a few other trains out there, but that's what I can think of off the top of my head.