There are some older oil fired boilers (or there used to be) and some gas turbine stations are dual fuel with oil fire capacity. They burn the fuel that is cheapest on any day. It used to be that natural gas was always cheaper, but these days I am not so sure.
There are many hundred oil-fired power plants. Most fossil plants are coal, many of the newer ones are natural gas - and almost all of the gas turbine plants are natural gas, but fuel oil plants are common.