Plant a Tree. It's Good For the Earth. Sometimes there is no backbone chain at all. Sometimes a polymer is built in such a way that branches just keep growing out of branches and more branches grow out of those branches. Dendrimers have unusual shapes which make pretty pictures, and really unusual properties.
Drug delivery is one possibility.
One silicon-based dendrimer can trap oxygen molecules in its branches. It is hoped that this can be someday used to make artificial blood. In the more immediate future, dendrimers might end up in coatings and as catalysts.