Don't just send a mail simply asking for freebies, or you'll never hear from them again! You'll have to work at it.
Try and cook up a nice little letter laced with a good bit of flattery. Search for any recent positive news/developments at that airline and use it as a talking point. If you can recount any personal memories with them or an "unforgettable" flight with them, it's probably even better. After all that sweet-talking, then it's time to mention any memorabilia (e.g. postcards) which they might have.
A few years ago, some of my friends sent out dozens of such letters to every major airline around the world they can think of. Mind you, real letters, not just e-mails (some $$ expense required, but they probably came across as a bit more sincere, especially in this day and age when few people write anymore). Naturally, a fair bit of customization of the letters were required for different airlines, so you can imagine the work required.
The results aren't too shabby either. Although many didn't respond or just sent back standard form-letters, a good number of them did send back at least something (postcards, sticker, buttons, etc). I recall the most generous of them all was the old Swissair, with one of my friend receiving a package with postcards, poster, Swiss chocolates, and even a small Swissair backpack!!!
Not sure how many airlines still print their own postcards nowadays or are still well-off enough to send such goodies, but it's worth the try. You never know what you might find in your mailbox one of these afternoons you got home from school!!