Glasses are not always glass! It used to be drinking vessels were called glasses if they were made of glass, metal, or clay. Nowadays, we have plastic, paper, and Styrofoam.
Disney collectible glasses most often are really made of glass. Many originally were given or offered at a low price for purchases made at Burger King or MacDonald. You can find individual glasses and sets for sale on eBay. A classic glass featuring Dumbo or Peter Pan might not be as expensive as you might think.
Of course, you can find plastic Disney collectible glasses and tumblers, and Sippy cups as well as Disney Antique glassware. Mickey remains the most popular character on glasses, but you can find Clarabelle, Pocahontas, Buzz Lightyear, Pinocchio, and Aladdin as well.