MMM has a recent post on some absurdly Bad Deals which arrived by way of his junk mail. I'm glad he could use it for a Mustachian rant.
I prefer not to receive junk mail. There's the odd leftover and seasonal election mail I can't seem to avoid, but mostly there just isn't any. (There's not much other paper mail, either, since most of my regular bills and statements are online these days.)
When Husband and I moved into our house, we started receiving loads of stuff for the previous owners: horse gear, cigarette company-branded apparel, you name it, and all wildly irrelevant to us. We also started getting stuff from the lists that apparently camp someone at the public records office to harvest addresses of new move-ins.
Anyway, if you haven't yet (and my apologies; this is for the US, and I haven't checked much for elsewhere), do get on the preference service list for the Direct Marketing Association
https://www.dmachoice.org/and register with
https://www.optoutprescreen.com so you stop getting most stuff. Give it a while to kick in (or out), and then start calling or digging online to request removal from whichever catalogs and mailers are still coming. Usually a search for "remove mailing list [company name]" will suggest something, even for the seemingly intractable things like sales circulars and coupon decks. Occasionally,
http://gethuman.com/ proves to be a valuable resource for getting through.
Someone in the comments suggests an app. I haven't tried any app or service, but if anyone has, I'd be curious how well it worked.
Oh, and by the way, if you're moving, think twice about filling out a forwarding order with the USPS. They sell the addresses. So do many surveys, drawings, and warranty cards*.
I know it's never going to happen entirely, but I envision my home as an advertising-free zone, and I'm more than happy to start by cutting off the influx of useless trash which is junk mail.
*Many years ago, as an experiment, my dad filled out a survey he found in either the junk mail or the newspaper inserts, in the name of a nonexistent family member he named George. We gave George an arbitrary assortment of tastes, possessions and hobbies, and sent the form back. George got all kinds of junk mail, including a hand-addressed come-on for a pyramid scheme (this was pre-Internet). George never answered a single ad or letter, but for all I know, he's still getting stuff. It was sure an eye-opener about how mailing lists get collected and sold.