The taxis are usually positionned in front of the Morges train station, you can also call them to pick you up somewhere. Other than in some countries, in Switzerland it is not common to stop a taxi in the street.
Morges Taxis Direct Morges St-Prex Sàrl
Passage de la Voûte
Tel. +41 (0)21 802 67 57
Fax +41 (0)21 802 67 58