Travelling to many countries requires you to have Visitors Health Insurance, for example, USA, the UK, Canada and Europe. Gaining (for example, the Schengen Visa for Europe) or maintaining (for example, the Exchange Scholar J Visa) a visa requires you to have Health Insurance. Any person travelling for the sake of pleasure, business or studies should obtain health insurance.
This is actually a very wise investment, because if you become sick away from home and you do not have Visitors Health Insurance, you may face a hospital bill much larger than your planned budget, leaving you either in debt or in a foreign jail.
It is particularly important for students to have Student Medical Insurance. While domestic health plans may help citizen students, Student Medical Insurance is even more important for visiting students, such as international students or participants of a student exchange program. Most countries require Student Medical Insurance to maintain the visa status. This includes the International Student F Visa and the Exchange scholar J Visa.
Also, students are not exactly (as the cliché goes) rolling in money. Besides paying course fees and accommodation or rent, paying up enormous hospital bills is not something they would want to do.