Are PhD scholarships and assistantships taxable? I'm currently in the process of applying for various scholarships to fund my PhD. 

Many scholarships mention explicitly the approximate amount per year of the scholarship. This is usually the amount excluding tuitions, so the amount mentioned is intended to be a stipend to cover living expenses.

I've never seen it mentioned anywhere, nor could I find a definite answer of this online: will this stipend be taxed? E.g., should I subtract a certain percentage off the scholarship amount that's mentioned, to calculate my real monthly income? Does this depend on the country the scholarship is given in, or are there international agreements on this?

I'm in the initial stages of setting up my PhD programme, therefore I'm in contact with professors in New Zealand, Australia, the United States and Canada, so ideally, answers to my question apply to any of these countries. If it's relevant: I'm a dual citizen (European/American Citizen).
Taxation does depend very much on the country, as well as the type of award you receive. The amounts similarly vary from nation to nation. To give two examples:


In the US, scholarships and fellowship stipends are taxed as ordinary income. However, in some cases, for externally funded awards, you need to be careful, as the university might not withhold taxes. In that case, however, you would need to make estimated tax payments, as you are still responsible for paying the tax "on time!" 
Don't forget that your tax burden may also include state and local income taxes, depending on where you live. Making matters even more complicated, cost of living fluctuates wildly: you're probably better off with a $25,000 award in the midwest than a $35,000 or $40,000 award in New York City.
In other countries, the system can vary. In Germany, for instance, graduate fellowships are not taxed, while "standard" graduate positions, which are considered employees of the state, are taxed. At the same time, however, people receiving the taxed positions receive health benefits and pay into the social security system. Stipend recipients are responsible for their own health insurance, and do not accrue time in the social security system.