We were getting so many catalogs in the mail, most of which we never and would never order from and even two of the same catalog on some days. Solution: Catalog Choice! It's a non-profit that gets grants and donations so it's FREE to you and me.
Just go to catalogchoice.org and make an account. Then sit down with your stack of magazines. You'll need to enter them one at a time and it does ask for limited info such as name of the recipient and address and catalog number. It can take up to 90 days for them to stop and, in some cases, you'll need to call the magazine's company direct to stop it, but this is a great start.
Catalog choice can even stop phone book and junk mail deliveries in some cases. A clean mailbox is a beautiful thing.