if they are beautiful quilts with sentimental value- there are people out there who restore old quilts- if you are interested in restoring them there is an option- if you really have no interest in these worn out quilts---well- all things loved and used wear out sooner or later- you could pass them on- to a thrift shop- or donate them to a humane society-
you could even give them to some kids to make forts-
i would not burn them- my kids and grand kids can always find a use - even if it's using them for a drop cloth-or to cover the wood pile- useful is useful....and if it's a rag already---no harm no foul.