Those are seed heads and I like them too.

In one of Mary Toomey's books she mentions one particular clematis benefiting from being deadheaded, but I don't know that they all do based on her comment.

You probably have a group 2 clematis, which is nearing the end of it's bloom season.

How long has it been blooming and what zone do you live in?

Any plant benefits from being deadhead...think about it..the energy output of the plant is great to create those seedheads...if you prune off the seed heads the plant can focus on growing more vines and flowers instead of the seedheads..the only purpose to allow seedheads is if you are wanting to collect the seeds for growing...Jeanne

Many plants that grow here will not rebloom even if deadheaded - Peonies, asiatic lilies, Amsonia, Astilbe, Siberian Iris, Oriental Poppies are examples. Most blooming shrubs will not rebloom and neither will fruit-bearing trees.

Also, there are plants that we can grow, which won't grow in the most southern parts of the States because they require a long chilling period.