The sad story is, for most mail you'll need to call customer service directly (often several times) and ask to be removed from their mailing lists. I started by making one call a day, and my junk mail has been considerably reduced. It also helps to not be put on the lists in the first place; sweepstakes, drawings, even warranty registrations are ways for companies to get your contact info, which they may then sell to other companies and mailing lists. Sure, you could win a five thousand dollar shopping spree, but it's more likely you'll end up with mail you didn't ask for and offers you don't want.
Decline to give your information at the register when you make purchases, uncheck boxes requesting permission to send you information, and only give to charities that will keep your information private (sadly, many charities, upon receiving your donation, will sell your information to mailing lists). Guard your address like your social security number; give it only to people and organizations you trust, and take reasonable precautions to make sure your information is being sent over a secure connection and that the recipient will keep it private.
It is possible to see a rapid decrease in junk mail by signing up with a few services, many free. You can put a stop to most credit card offers by going to www.optoutprescreen.com, a site run by the three major credit reporting agencies (Equifax, Experian, and Transunion) which can stop "firm" offers of credit for either five years or permanently, depending on the method you use (a mail-in form is required to stop offers permanently). By going to the Direct Marketing Association's webpage, you can request that your name be removed from their lists and affiliate member's lists(though you'll need to register with them, an annoying step). Lastly, the independent organization Catalog Choice will contact companies you list on your behalf and request that you be removed from their mailing lists (a registration is also required for this site, though it can be done through Facebook). Catalog Choice also offers escalating layers of protection and convenience in stopping junk mail for nominal fees. For thirty-five dollars, the company 41 Pounds will guarantee the removal of your name from all junk mail lists for five years.
Remember, by stopping junk mail you'll save paper and plastic waste from entering the environment, avoid wasting your own time each day corralling paper clutter, and let companies know that you, and others, aren't interested in their wasteful practices. Yes, there is initial time investment to keep junk mail from getting to you, but it's nothing compared to the feeling of getting only mail you actually look forward to.
First time reading about a hundred steps to zero waste? Go here for the introduction and index.