The World Health Organization maintains a real-time dashboard providing an overview of the COVID-19 situation here https://experience.arcgis.com/experience/685d0ace521648f8a5beeeee1b9125cd
Their data is updated live and can be accessed here: https://data.humdata.org/dataset/coronavirus-covid-19-cases-and-deaths
A number of humanitarian organizations are publishing data about different aspects of the global and country-level response to COVID-19. Many of these resources are available in a dedicated COVID-19 crisis page on the Humanitarian Data Exchange.
Many national health authorities also provide updates on a daily basis. Visit your national health authority's website for more information.