The only two I would suggest watching in order would be the two Renaissance episodes. Otherwise, they really don't have to be viewed in order. I have to say I found the Renaissance episodes and Matriculated to be the most informative as far as the background of the Matrix. The Kid's Story is interesting too.
I haven't seen all the animatrix stuff but as far as i know they contribute somehow to the story, so far i've only seen "The last flight of the osiris" and it was cool as hell, as i understand there is already a DVD out containing all these animation shorts and the soundtrack of The Matrix: Reloaded.
Question: this kid who worships Neo on "reloaded" comes from one of these Animatrix?
I watched all the Animatrix on Pay Per View on cable. The Renaissance episodes show you how the machines came into power and how humans became their power source. They are pretty graphic for animation. The one called "Matriculated" gives you some insight on how the Matrix came into existence. The one about the Kid just tells you how he became unplugged. The others just give you different perspectives on the Matrix. I don't think they are necessary to understand the movies, but they are very helpful.