The Kinks V's Yo La Tengo
Here's another old Mojo magazine CD post. This post is from the March 2006 issue which (amongst other things) looks at the history of The Kinks and Ray Davies.
Yo La Tengo have played gigs with Ray Davies and even recorded as his backing band. They have also recorded a few cover versions of Davies/Kinks songs in their 20+ years
For some more Kinks covers, check out radams ad nauseum post.