I agree that a single-row undercoat rake is essential -- I've spent too much money on too many latest-greatest, new tools, only to go back to the old, well-worn undercoat rake I bought for a few bucks at least 10 years ago.
It's the right tool when they start to blow their coat and get those undercoat tufts that make them look scruffy. Be gentle, and do short sessions several days in a row -- work mats like you're eating a row of corn on the cob, all the way across a narrow row you've chosen, then up and and across the next row, not attacking the whole mat. That way you're separating the mat from the edge, and releasing the old fur. (I'm not a groomer -- I'm just telling you what works for very thick coats and sensitive-skinned dogs.)
For reasons I haven't figured out, the undercoat rakes with two rows of teeth don't work as well as the simple single-row type. I truly don't know why.
I also love having a Kong Zoom Groom around. Or rather, my dogs love having that thing around. You can move it in circles to get surface hair, and every dog seems to think it's a massage once you start on the shoulders. For dogs who aren't fans of brushing, that's the one tool they all like.
I have a Furminator, but I've never been all that impressed with it.