Dissecting their repair mechanisms might give us insights into regenerative medicine in the near future, and technical knowledge for suspended animation for long distance transport or generation jumping in the not-so-near future.
Relatedly, note that storing information in DNA is the longest lived form of information storage. Harddrives tend to deteriorate in ~10 years or so. Flash Memory has a similar life time. Books can last hundreds to thousands of years, but no more, and stones and rocks and fossils, perhaps a few hundreds of millions of years. But genetic information can be maintained for billions of years--it is a discrete information encoding, is easily copyable, and has noise tolerance and error correction. Not very useful (yet!) to store information and data, but very interesting to think about conceptually: humans have been reconstructing in metal and silicon what nature developed billions of years ago. Sort of cool to think about.
And yet some creatures are believed to be immortal while being "very alive".
If you found this interesting you might also enjoy a TED talk by Rachel Sussman entitled "The world's oldest living things":
Aside: There seems to be some poignant commentary crying to be wrested from the above, but I'm unable to pry it off. Anyone else?