In 2012, the Secretariat of the Convention on Biological Diversity (CBD) along with the Science and Technical Advisory Panel from the Global Environment Facility (GEF), published an awesome report looking at the interactions between species and plastic. They reported that 663 species (15% of which are red listed by the IUCN) were found to interact with plastic in the ocean. This was up 40% from the previous review (Last, 1997).
The new AWI Litterbase Portal complies marine debris research from around the world, analyzing and mapping surveys and data. They have found that 1,220 species are being effected by marine debris. Up more than 50% from the 2012 study.
I doubt that there are any marine species who are not interacting with plastic on a daily basis. But instead imagine that this trend is partially due to the fact that research is taking a broader look at animals. Instead of focusing on turtles and sea birds, as much of the initial research did, we are starting to see papers looking at sharks and oysters. As we study more and more species, I imagine this count will continue to rise.
Read more about the AWI analysis here