In the early 1990s, I spent a few months in R.I., and became rather fond of coffee syrup. I tend to add it to my coffee instead of granulated sugar. It adds sweetness, as well as intensifying the depth of the coffee flavor.
Coffee syrup is also pretty good drizzled over ice cream or frozen yogurt. Rhode Islanders use coffee syrup mostly to make what they call "coffee milk," which is a glass of milk with a few spoonfuls of coffee syrup stirred in.