The Cure are a kind of alternative Grateful Dead, inspiring worshipful devotion in their fans, and bewilderment in the rest of the population. Though I admit to being in the second camp, the ones largely unmoved by Robert Smith's tummy-ache vocals, I enjoy a kooky Kure kover, and coincidentaly there have been several coming my way lately:
Rockabye Baby: "Close To You" - From "Lullabye Renditions of The Cure"
The Supersonicos: "Killing An Arab" - Surf guitar RAWK, even throws in some "Miserlou." This band is from Uruguay (!), and "The Supersonicos" is how "The Jetsons" is translated into Spanish.
I suppose The Fall could also be considered an alternative Grateful Dead, but I haven't heard any kooky Fall kovers.