A certain application for permanent residency in Canada requires submission of the results from one of several English language proficiency tests, like this one. Are tests like this easy for native speakers? I have lived in the US for many years and English is my native language. Should I buy the study materials? I wonder if it would be a waste of money.
To answer the top-line question -- no, if you're a native English speaker the tests should be no more difficult that anything you'd encounter in day to day life.
Also, there's plenty of free test materials if you want to convince yourself of this, here's some practice stuff from the Canadian Academic English Language Assessment and here's another one generic proficiency test.
These tests are to prove you can get along with general English (speaking, reading, and writing) enough to cope with day-to-day interactions. They're not designed to prove some deep college level understanding of the subtleties of the English language.
There may be some quirks of grammar or understanding that you get wrong depending where you learnt English (i.e. American English vs British English vs Canadian English), but you should pass the test easily -- just the fact that you wrote the question properly proves that.
You may want to practice first, if you're worried, but there are plenty of free resources -- definitely don't go paying for study material. You might also want to read through this (2010) thread for more info.