How is the "r" sound pronounced? One of the most trickiest sounds to pronounce correctly in Mandarin seems to be the "r" sound, as in 日本 (rì běn). It's not uncommon to hear people pronounce that like "urban."

I have been told it's not supposed to be pronounced like the English "r" like in "red" (alveolar approximant). Some say it's closer to the French "j" in "jour" (voiced palato-alveolar sibilant).

What is the correct way to pronounce the Chinese "r"?
I suggest you pronounce it like the "r" sound in "brrrrrrrr I'm cold" or "grrrrrrrr I'm angry".

So for Japan you could do it like "rrrrrrr ben". 

Don't roll this "r" sound. This will get you about 80% accuracy. To get the rest you need to make the same voiced palato-alveolar sibilant, then you will be there.

Just want to add the palato-alveolar sibilant in the French "j" is made in a different part of the mouth to the Chinese "r". The "r" sound should be at the roof of the mouth.

Here is a great video on youtube to help: http://www.youtube.com/watch?v=_D6G0aqjtso