In many big cities that have some form of rapid transit (i.e. subway, grade-separated tram network or similar) combined with various policies discouraging car use, public transport is more popular than car for intra-city trips. Some of the best examples are Paris, Munich, Zurich, Vienna, Amsterdam, Copenhagen (in the latter two, cycling is the most popular mode of transport) and others.
For longer journeys, public transport is very popular in countries that have extensive high-speed rail network and very expensive motorways (France, Spain and Italy). However, more people still travel by car.
Additionally, public transport is more popular than cars in areas where cars cannot get, such as Venice or several car-free villages of Switzerland, most notably Zermatt. :-)