Actually, you're more limited by shipping requirements than Mormon rules. It would help to know where he's serving, but I'll just generalize.
You shouldn't send books or movies, because he can't use them. Gift cards are probably not the best idea unless you know exactly what shops are in his area, which is difficult considering the fact that he might be in another area by the time the package arrives.
Still...my brother is on a mission in South America, and while that does limit what we can send him, maybe some of my ideas will help you.
First, we decided to send him a bunch of random things. You may not want to send very much, but if you run down to the post office, you can get a small flat rate box. The smaller ones only cost about ten dollars to send (it may be as high as $13, though I think you can find smaller ones). Anything you can cram inside will go for that price, so it's really not bad, and it can be cheaper than trying to send a present through the mail.
As for gifts...he's majorly into sports, so we found a bunch of Lakers gear for him (hats, stuff for the walls, ect.) He can't wear the hat or shirts when he's doing missionary work, but he wears them around the apartment and when he's out doing service, so they're worth sending. If your friend is also into sports, you might think of something similar.
Candy. My brother can't really get candy where he is, at least not American candy, so we sent a bunch of his favorites. This isn't really necessary if your friend is in America, but then again, he might not be able to afford candy on his budget. Missionaries are only given so much a month, and it's not really enough to support a sweet tooth. He would probably appreciate it.
Just be careful about sending chocolate. My mother used to send my favorite chocolate to me all the time when I was a missionary, and it always arrived in a melted, inedible mess. You probably don't have to worry so much since it's winter, but still...
A package of Christmas lights. I know that seems cheesy, but I loved getting that myself, and I'm not even into Christmas. I strung them up around my apartment and would giggle every time I turned them on (I was in that apartment for six months, and I never took them down). I sent some to my brother last year, and he had the same reaction.
Stationary. Again, possibly cheesy, but missionaries stay in contact through letters, and he may be glad to have some nice stationary/envelopes.
Scripture markers. Missionaries do a LOT of marking in their scriptures, so they're always in need of good crayons. If you go to Wal-Mart, you can find a plastic box with those long, twistable crayons. Those are perfect, and they're fairly cheap.
Also, if you shared many of the same friends, you could get a cheap tape recorder and go around and get them to record short messages for him, then send him the recorder and maybe a spare tape (in case he wants to reply). I received that one year from a friend, and I really loved it.
Anything personal that he would like. I'm not sure what his tastes are, but as long as it's not a DVD or book, he can probably use it. Just make sure it's not something inappropriate, obviously (I had a friend who was sent a blow-up girl. Hilarious, but probably not the best gift).
Oh, and his family might be sending him one of those tiny Christmas trees. Ask if they are, because you can always get him some kind of decoration for the tree if you're absolutely unable to come up with any other ideas.
I can't think of anything else, but if you come up with something yourself and aren't sure if it's missionary-acceptable, feel free to email me. I'm happy to help.