Sure they do. I've got a Sansa Clip that I bought back in 2008 for $50 that's still going strong, especially now that I've loaded Rockbox on it and it can play formats other than MP3. iPods especially are famous for basically living forever, especially if you flash-mod them (replace the hard drive with something solid state, like an SD card), possibly also replacing the battery if it's stopped holding a charge.

DIY repair work isn't for everyone, but it doesn't get much easier than fixing an old iPod (the older the better).