Not much.. probaly timetables, and postcards. ALL major airliners have their own licensed merchandise shops where you can BUY model planes, clothing, bags, cards, luggage tags and lots of other items with hte companys logo. I know Northwest, American, USAirways have a shop online. You most likely will NOT get anything from major airliners in the US and Canada.. you'll have better lucky with smaller international carriers. The email addresses can be found on all their sites.. look for a 'contact us' link..
If you REALLY want something from a particular airline, BUY it and don't be cheap by trying to go after free stuff.