There might be audio treasures stashed in a relative's record collection, but only if you can restore the discs to less topographic conditions. Wired's How-To Wiki offers a guide to restoring that warped vinyl with careful heat application.
Image from Positive Feedback.
There's no one guaranteed method to getting records back into shape, because different records have been moulded from different vinyl mixtures and been exposed to a wide range of storage conditions. That said, the "LP sandwich" described by Wired requires only two sheets of flat glass and the patience to watch a record in an oven set at 200F/93C. If that sounds a bit too risky for your really good discs, there's also a method that uses gradual warming from direct sunlight:
Use the same method as above, and put the LP sandwich in direct sunlight. The glass will slowly heat up and the vinyl will begin to soften. If the glass doesn't seem heavy enough to press the LP flat, find a weight (a can of soup or some such) to press it down in the middle. Normally, 10-15 minutes is long enough to heat the vinyl. After it's cooked, let it cool and give it a spin.
Have you fixed any of your own warped records using the "LP sandwich"? Got another method that seems to work better? Spill your best practices on ancient platters in the comments.
Fix a Warped Record [Wired How-To Wiki]