I saw many of these on my big old Rosa rugosa bush yesterday. What are they?
This looks like a gall. At first I thought that it was the common rose bedeguar gall, also known as Robin's pincushion gall which is caused by Diplolepsis rosae, a small wasp. However, there is a related wasp, the spiny rose stem gall wasp Diplolepsis spinosa, which attacks Rosa rugosa so I imagine this is what you have here.
Incidentally, you are probably wondering what bedeguar might mean. According to the OED it derives from a French word bédégar which in turn comes from the Persian bād-āwar ('wind-brought’).
This is a stem gall induced by the cynipid wasp Diplolepis spinosa. It has moved from the wild rose Rosa blanda in eastern Canada and Rosa woodsii in western Canada, onto the introduced Rosa rugosa. The bedegular or Robin's pincushion gall is induced by Diplolepis rosae. Both the host dog rose and D. rosae have been introduced from Europe. The mossy gall of D. rosae is induced on leaf tissues - even though the gall looks like it comes from stem tissues.