The 80's, yeah, they existed. The proof is the pile of cassette tapes you laboriously made and coveted back in the day. But do you use them now? Nope. They're taking up space, and as all clutter, it's a weight in your life. It's best to dispose of clutter to free up space in your life for new things, supposedly. If nothing else getting rid of your old cassette tapes will free up space in a cupboard or cabinet and it's up to you whether to fill it with something else, or to enjoy the empty space.
Normalthink would have you simply toss the stuff into the trash and forget about it. But as someone who thinks about long term effects of my actions I want to do the responsible thing. Cassette tapes are made of plastic, plastic contains nasty chemicals and just throwing it away will aid and abet the escape of those chemicals into the environment. It would be better, now that those bits of plasticy thingy's exist, to ensure the chemicals get sequestered somewhere appropriate.
One may find themselves clinging to specific tapes. Being cassette tapes the recording may have sentimental meaning. But is sentimental meaning a reason to keep it around? Maybe first one should get the same recording on newer media or digitize it, so that you can dispose of the cassette tape.
Clinging to things is one way that clutter builds in ones life, is it not?
The first thing to consider is reusing the tapes or handing them to someone who will take care of them. But being cassette tapes the chances of that is somewhere between slim and none. That probably means you'll decide to dispose of the tapes, so lets move on to the best disposal method.
There are various crafts or widgets one can make out of old cassette tapes. The tape can be a ribbon or used to tie things up. But if you think about it that only delays the inevitable need to avoid throwing the stuff into the trash. The goal is to avoid sending stuff to the landfill.
Green Disk (http://www.greendisk.com/) can recycle a wide variety of what they call "technotrash". It's implemented as a "technotrash can" for collecting up to 70 lbs of stuff, and one puts in their office. After collecting a full can, you ship it to Green Disk office. Obviously this is not suitable for an individual to recycle a few tapes, but for a business to properly dispose of stuff.
Green Citizen (http://greencitizen.com/what_we_recycle.php) recycles a wide variety of electronic stuff including tapes. They charge $.50 per pound.
Our Earth (http://www.ourearth.org/recycling/) contains a directory of recycling programs that is an excellent way to find the place for you, especially their extensive list of "Curbside and local programs". Another good resource is your city whose website probably includes a directory of recycling programs.