Well, I would be likelier to adopt a dog who's history I knew. Papers only give you a link to their past, they can still be puppy mill pups
. But you have a better chance of tracing it if the dog is registered.
I wouldn't overlook a good dog just because he didn't have papers, though. Anna was a rescue and came without papers. She's the best anyone could ask for.
In some breeds, health issues are a real concern. In german shepherds, for instance, registering parentage helps keep track of their OFA classification. A dog with clear hips is alot more adoptable than one with poor hips. Their registration is the easiest, cheapest, and first indicator of what to expect here. When you get the papers back, you'll have a record of the OFA history in your dog's lineage. (if the breeders bothered OFA'ing them).
Papers don't make the dog good or bad, but papers can pressure breeders to be a little bit more responsible. In the overall wellbeing of doggies around the world, I don't see the reason not to register, even if you never breed. You'll get a little magazine for your troubles. I would defenitely micro chip though. that's the only real important little piece of 'paper' you want
.