A very long time ago some of the Darkthrone tracks I downloaded from Napster were corrupted and had glitches/noise in them. I didn't know they were glitches, and I listened to this for years and thought it sounded great. I actually regret not having those "damaged" MP3s any more.
60s-era blues is another good example. The recording equipment at the time certainly wasn't bad, but it was not yet perfected. It added a certain sound to recordings from the time that I kind of miss in later recordings.