If the different flights are in the same booking, the baggage will usually be transported to the next airplane automatically. There are exceptional countries (e.g. US) where the passenger has to pick up the baggage and check it in again.
If the flights are booked separately or from a budget airline, the passenger usually has to pick up the baggage and check it in again at every airport. We recommend passengers to contact the airline companies in advance to avoid problems at the airport(s).