What I recommend to my clients for dealing with magazines is to first sort the magazines you receive by those that you "love to read" and those that you "never have time to read."
For those that you "never have time to read," consider calling and asking to cancel or switch your subscription. Often magazines have affiliations and you can simply select another title. Alternatively, you can donate them to a local dentist, doctor, or other practice with a waiting room until your current subscription runs out. (It's great to recycle them but better to reuse them first!)
For those that you "love to read," organize the magazines that you have not read yet in a magazine file, only keeping the last 1-3 issues. As you read a magazine, tear out articles of interest and organize them by topic in a binder or expandable file. Topics may include: Health, Recipes, Mommy Tips, Crafts, etc. Once you are finished reading that magazine and have selected (and filed) your articles, recycle it.