That basically applies to numbers, rather than to variables, and comes from the days when you would have to choose between dividing (by hand) 1 by [MATH]\sqrt{2}[/MATH], or [MATH]\sqrt{2}[/MATH] by 2. The latter is far easier! (Try it. And then try again with more decimal places.)
Today, I think the main reason it is commonly considered standard to rationalize denominators is so that there is a standard form to compare students' answers to. It's also needed when you add two radical expressions together. But there are many cases where the rationalized form of an expression is far less simple, and I would never do it unless I had some specific reason to.