Their video for "Soon" is heartbreakingly beautiful and haunting, really providing a refresh to the power of the original:
Athens band Japancakes have also released an instrumental cover of the entire Loveless album. I've used tracks from it for audio zippers during station breaks on the show. While not actually a video, you can listen to their cover of "Only Shallow" here:
Japancakes' MySpace (linked above) also has a cover of The Cocteau Twins' "Heaven or Las Vegas".