So one option would be to reuse them...
There are some cool ideas for projects with slides and X-rays if you are a creative soul.
Others may also collect them to reuse in art projects, as these posts on Flicker and this site in the UK show. Maybe local artists or art teachers could be interested in having them for their projects.
If the slides have some historical value, donating to a museum would be a great option not only to honor the ones in the photos (or who took them) but also to document events and contribute to the knowledge and research of others. Once we donated some filming equipment to the Brevard Museum of History & Natural Science. There are other museums in Brevard County that may be interested in adding slides to their collection.
Another alternative is to sell them for reuse: Etsy and Ebay have some slides for sale.
If reusing is not an option, you can safely dispose of them...
There was nothing on our county's website, recyclopedia or hazardous waste page, but after calling Hazardous Waste at (321) 633-1888 (email James.Fleming@BrevardFL.gov), we confirmed that they do accept boxes of photo slides. They are open Mon-Sat, 8am to 4pm. The three locations listed on their website would take them.
Next time you find those old slides and X-rays, do not toss them. Choose the best option for you and discard them responsibly.
Reduce, Reuse and Recycle, Brevard!