This depends on your visa and the availability at a school.
Australia – Yes you can. If you change before your arrival, you will need new confirmation documents, which you must show upon your arrival to the country. After your arrival, you can also change your course.
Canada – Yes, unless you are taking a Work and Study course, which requires a work permit.
USA – Once your I20 has been issued, you cannot change your course. After arrival, you can extend your course or change to another program.
UK, Ireland & New Zealand – Yes you can, before your arrival. You will need new confirmation documents, which must show upon your arrival to the country.
Tourist Visa, USA – You cannot change your course.
Tourist Visa, UK – You cannot study in the UK on a tourist visa.