While individual states and localities have taken it upon themselves to report the number of cases, deaths and outbreaks of COVID-19, and now the number of vaccine doses given, very few national and international groups are aggregating the data.
Perhaps the most famous source of aggregated information on COVID-19 cases is Johns Hopkins University and . Another group that has been keeping good numbers by aggregating data from many different sources are the folks over at Our World in Data. They have published a dashboard showing the number of COVID-19 vaccines of all types and brands given in the world. All of those data are based on what is reported by official sources, of course. As a result, some data may not be included if it is not reported or is reported by unofficial sources.
to explore the dashboard.