I get a ton of them, by virtue of being a physician. Time, Sports Illustrated, Money, National Geographic, just to name a few.
All these magazines think I’m sticking their products in the waiting room. Not so, in my case. They go into the break room, then into the trash.
This is very likely exactly what it is. They’re likely buying your name from a mailing list of people who look like their subscriber base.
I’ve had this happen to me three times in the past 10 years:
Rolling Stone started showing up in my mailbox. I figured that someone had given it to me as a gift, but no one ever acknowledged that they had. It was down for a one-year subscription, and they eventually sent me a renewal notice. I really enjoyed the magazine, so I did renew it (and have kept the subscription up).
Three years ago or so, Popular Mechanics started showing up. I’ve glanced at an issue or two, but don’t really care for it. I’ve never gotten a renewal notice, it just keeps coming.
Then, about a year and a half ago, I got an issue of Field and Stream. I have no interest in that magazine whatsoever, and I actually called their customer service number. The very nice CS rep said that, yes, they send out complimentary subscriptions to prospective subscribers, but when I told her that there was no way that I’d be subscribing, and that sending me the rest of the issues would be a complete waste, she graciously cancelled it.
Many years ago, I read about a guy who got himself a PO box and told all of his friends that if they wanted him to get their mail that they had to send it there. He then used his regular address and signed up for every free magazine, free newspaper, and free junk-mail thing that he could find. He had a wood burning stove, and used all of the junk mail and magazines to heat his house with all winter long. Free heating fuel. 
With the rise of the internet, junk mailers stopped sending out paper and send out junk e-mails instead. I don’t know if you can get enough free coupons and magazines these days to heat your house with. If I had a wood burning stove I might be tempted to try it.
I got the magazine, More, for years, even though I contacted them numerous times to tell them to stop sending me the damned thing. The magazine eventually folded and they stopped.
So cross your finger the magazine folds (except for Better Homes and Gardens, which is one of my favorite magazines).
Postage would be a killer. I wouldn’t wish that on anyone.
Just send me cash and I’ll buy them myself. 
You could always print out the junk e-mails and burn them.
I’ve been doing this for years now with my gf’s ex-husband’s mail. We do not know his whereabouts. If the return postage is paid, I write a note explaining how poor Pete has passed on, and getting mail addressed to him causes no end of grief for his poor wida.
It does seem to work.
Places like Slickdeals post freebie magazine subs.
But there’s usually a catch (or 2 or 3 …). Some require signing into a “rewards” program. Or worse, require you have some “friends” sign up too. The better deals are very transient. Once you see them they’ve been, um, “sold” (?) out. All available subs taken.
We got offers for free subs from various companies we’ve dealt with. I’d love to get a couple of magazine subscriptions. But these lists never have anything remotely like I’d want.
I used to write “Deceased” on the mailing label and put them back in the mailbox. I understand the Post Office no longer return magazines, though.
I’m getting Seventeen as if I subscribed. Never. Not even when I was 15. I just dump them in the recycle bin. I also used to get Parents magazine, which I think my SIL may have given me as a mean joke. Those, I would drop off at the hair salon because their reading material was seriously outdated.
I tried cancelling it. The person at the subscriptions office sympathized with me and was able to cancel one of the two subscriptions of Parents. She thought it was somebody who was doing a promotional sales fundraiser for their school and they didn’t want to ring doorbells, so they just jotted down some neighbors names and addresses and ponied up the subscription money themselves to make it look like they tried. Interesting theory.
You might want to try what my doctor does: he keeps them in a storage closet for five to ten years, then puts them in the waiting room.
Very effective with People magazine: “Hey, Angelina Jolie in a wedding dress. I didn’t know she was getting married…”
Quite a few years back I mysteriously started receiving Newsweek. I called up their circulation department and found out it was because I had bought a t-shirt from Allposters.
Yes, your clients would turn the blow-in cards into shivs, and fashion billy clubs out of the rest of the magazines and beat each other to death.
