By law, anyone living in the Netherlands for any period of time must have insurance for medical expenses. Depending on your situation, you will either have to take out Dutch public healthcare insurance, private healthcare insurance or you can use a Health Insurance Card.
If you are only staying in the Netherlands for study purposes (i.e. you are not doing an internship or working alongside your study) and you are from the EU, EEA or Switzerland, you can use the EU Health Insurance Card. The Netherlands has health insurance treaties with these countries, meaning that your national health insurance policy in your home country covers your stay in the Netherlands. If you are not from the EU, EEA or Switzerland, check whether your current policy covers your stay. If not, take out a special insurance for your stay in the Netherlands.
Be careful - this information is subject to change! For more up-to-date information about health insurance and specific circumstances check out www.studyinholland.nl. If you have any questions, contact the International Relations Office at Leiden University.
As a student, you can have a student health insurance, for example, one by AON. It costs around 40€ / month, or less if you already have a European Health Insurance Card (for EU nationals, ask in your country how to obtain one).
If you start working here, you'll need a Dutch Health Insurance, as required by law. This costs around €100/month and is, in quite some aspects, different than the student health insurance. There are many companies with which you can get one. We strongly reccommend you to contact the International Student Advisor for this. It will save you a lot of time, as everything (yes, everything) you have to read or sign is in Dutch, and the University can also help you with getting a subsidy which balances the costs for this (called 'zorgtoeslag' in Dutch).
I have a health insurance, but I received a letter from something called CVZ in Dutch...
Most international students encounter the "dreaded" letter from the CVZ, this is a letter in Dutch stating you will be fined if you do not comply by getting Dutch health insurance, this usually sends an international student into panic, fear not! Follow the instructions here in this case.
Please do NOT ignore this letter, inaction results in a fine, and this is a very tedious and difficult procedure to reverse.