The United Nations Office on Drugs and Crime maintains a spreadsheet of total persons held in prisons drawn from national statistical agencies.
The World Prison Brief publishes a list of totals and rates of prison populations as well as pre-trial/remand imprisonment, though notes that this is incomplete.
The Global Detention Project hosts country profiles that include statistics about the number and demographic information of individuals held in immigration or criminal detention.
Data on criminal, administrative, migrant, and psychiatric detention may be available at the country level.