There are stores that may buy them from you.

It also depends on what kind of shape the lps are in, and the qualitly of the recording, and the artist.

You could flog them on E bay or Amazon; there's lots of outlets for them.
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I you can't sell them on eBay or CL, Goodwill will take them.

What type of music do you have. Depending what they are you may be able to sell them. I have a friend that makes his living buying and selling old vinyl.

do you happen to live in the Chicago area?

Vinyl is making a comeback. Plus, some of the old stuff has never been released digitally.

Most cities will probably have somebody that deals in old vinyl - depending upon what you have, it might be worthless, or it could be a treasure.

Brookstone has a converter which is easy to use

Here is a link that might be useful: convert lps

Half Price Books will buy them from you if you have them in your area. You won't get rich doing this, but it's easy and they won't end up in a landfill.

I got really lucky and found a very good friend who loves, loves, loves playing old LP's and he has agreed to take, cherish, and enjoy playing my cherished Beatles albums along with others from the late 60s and early 70s. I may even be able to enjoy hearing them sometime when visiting at his house. I feel they are going to a very good home.