Sell some of your DVDs. You can get rid of them at a garage sale, through newspaper classified advertisements or online via an e-commerce site such as eBay or Craigslist. You might not make much money, but it's better than throwing them away.
Donate movies to a tax-free establishment, such as a school or library. Not only will this help you downsize your collection, you'll also get a tax break for the fair value of the donation.
Use a free ripping program, such as "DVD Rip," to copy your movies and other files to a computer hard drive. You can also copy DVDs to an external hard drive for more compact and portable storage.