Used to ship paper products from New Jersey to California, Oregon, and Washington, in containers. Can't imagine a much longer haul than that. I suppose the paper makers in Maine probably ship further, to the same destinations.
Now that Mexico makes most of our "American" cars, I would,bet some of those railcars move several thousand miles.
Prior to deregulation in 1980, shipments of lumber were entitled to "open routing," meaning that a shipper could specify any route possible using established interchange points. A common practice on West Coast lumber was to ship a car to a more-or-less random destination in the East, consigned to the shipper, and then get on the phone to find a buyer somewhere in the East; the longer the route, the more time he would have to find one (if the car had to be held somewhere en route until a customer was found, there was a charge per day until the railroad received final disposition--as long as the car was moving there was no charge). This practice was known on the railroad, tongue-in-cheek, as "seasoning in transit." When the shipper found a buyer, he would trace the car's movements with the various railroads, and when he found it would issue a diversion order changing the destination to the buyer's location, usually adding that "they need it right away." In the 1950's when I was a trace clerk in Boston, I got involved with a car from Oregon which had been routed to cross over itself--somewhere like Iowa it turned south through Missouri, then westward through Kansas and back through Nebraska, through Iowa again, etc., en route to its final destination in Massachusetts. (This was all included in the through rate, the same as if it moved over a direct route; guess how much all the participating carriers made on that one.) Circuitous routes on West Coast lumber were common, although I have an idea that that one would be a contender for the gold. In today's operation my guess would be that the longest consistent routes on the greatest amount of traffic would be doublestack trainloads of mini-landbridge containers from West Coast ports to East Coast population centers.
A recent issue -- I saw it at a bookstore a few days ago -- of one of the British Rail-interest magazines had an item about the arrival of rail freight from (I think) China in Britain. I don't know what happened at breaks of gauge (China and Western Europe use standard -- 4 foot 8.5 inch -- gauge track, but the ex-Soviet railways use 5 foot gauge): since the freight was containerized, it may have been simplest to switch the containers to different flatcars. In the past, however, cars with trucks allowing the wheels to be moved along the axle have been used on some rail routes that cross breaks of gauge, and if this was done it would be about the longest possible routing for a freight car (on Earth's railways...).
F.w.i.w…. Wikipedia says that Moscow to Vladivostok is 5772 miles by the Trans-Siberian Railway. (And Moscow to St. Petersburg is 403 miles: Russian railways make possible a plausible, non-circuitous, route for a freight car of over 6000 miles.) For comparison, Los Angeles to the East Coast in the U.S.A…. Well, for passengers (Amtrak's Southwest Chief from LA to Chicago and then the Lake Shore to New York) it's about 3225 miles: a bit over half the coast to coast rail distance in Russia.