Slicker brushes are your friend.
And a bottle of Show Sheen. The very full-coated Aussie I housesit for got COVERED in burrs one day. I plopped down in front of the TV with his slicker brush and the Show Sheen and had them all out in less than an hour. The ball of burrs I had when I was done was seriously about the size of my head. Those fluffy butt hairs hold a LOT.