That is a very loaded question with along history. Back in the day, ATSF paid Lionel to make models of their F-units. That kind of cooperation is lost on most modern RR's.
As of today, CSX, UP, and Amtrak all have licensing agreements. NS does not. BNSF, if they have one, is pretty loose about it. I don't think any Canadian roads do. KCS...I've never heard of anyone mentioning them with licensing. That's all the Class I RR's. I've never heard of a Regional or Short Line have any kind of licensing agreements with anyone (they seem to be happy that they get any publicity at all). There are some very touchy commuter agencies (being gov't bodies, of course). I hear Metro-North is one of the most sensitive, while I don't think anyone at the MBTA could care less.
Chessie/CSX raised a big stink in the early 1980's by trying to limit the use of their logos on all model railroad equipment. At the time, the big names in the hobby appealed to the public, and after a front page article in the New York Times lambasted Chessie/CSX for picking on the little guys, Chessie/CSX backed down and created a simple licensing agreement that's something like $1 per year that CSX carries on to this day.
UP, around 6 or 7 years ago, at the possible urging of Overland Models/Tower55 (who wanted an exclusive deal), tried to start their own licensing program that was almost ruinious. It involved not only their own logo, but every predecessor and every predecessor's predecessor all the way back to the pre-Civil War era. It made manufacturers sign up and either give UP around 5% of the model's cost, or approx. 5% of their entire company's income (which meant UP would get to look at their books). They also demanded payment for past releases from companies like Microscale Decals. UP also demanded prior approval for all model railroad items using production models only (no pre-production models allowed). In short, it was a fiasco. Only after a change of CEO's and a possible expensive legal fight from MTH (of all people), UP changed their policy to a more simple program that did not demand excessive cash from model manufacturers. Amtrak has signed two exclusive licensing agreements: one with Walthers and one with Bachmann. Walthers holds the exclusive rights to all Amtrak paint schemes after Phase IV (large blue band with small red and white stripes). So any Phase V "blob", Phase VI (like Phase IV but with reflective stripes and new Amtrak logo), and anything with the new Amtrak "3 sheets to the wind" logo has to have permission from Walthers (who have granted it from time to time to Athearn and Overland). Bachmann holds the exclusive rights to the Acela train sets and the HHP-8 electric locos. Fortunately, Bachmann did a very nice job on these, so it's no big deal.
BNSF is kind of questionable. I recall a brass importer had a shipment of Santa Fe steam locos seized by US Customs because on the sides of the shipping boxes they said "Santa Fe". US Customs officials called BNSF and asked them if they knew about it, and of course BNSF said, "No." These new brass HO models were then tied up for quite a while while the poor importer had to deal with both BNSF and US Customs to get his shipment out of impound. I don't think BNSF has a set policy in place, but you can bet every shipment from overseas does not say a railroad name anywhere on it.
Most RR's are happy to have their railroad modeled. Only a few are paranoid enough to want to limit their use. You know, the "What if little Johnny swallows that loco with our name on it? They could sue us!" kind of hooey.
Paul A. Cutler III
You might find this link interesting regarding the payment of royalties:
http://www.trains.com/mrr/default.aspx?c=a&id=907
Alton Junction
Yes, that was the big nasty lawsuit a couple of years ago, and little MTH won out over the BIG railroad. Their victory was extended to the entire model railroad industry, thus saving us modelers a lot of money in license fees passed on to us by the manufacturers and allowing a lot of road names to be produced by companies who were not anxious to pay license fees on every item they manufactured.
George In Midcoast Maine, 'bout halfway up the Rockland branch