Though it looks like a normal sponge, the Gonzo Pet Hair Lifter – a brick of latex mattress material – has a peculiar tacky texture. It's easy to mistake for other "clever" sponge products, such as those covered in suede, cellulose or microfiber or whatever, but it's much better for dealing with fuzz. It's the most effective thing for dealing with dog hair I've ever tried, in fact, and I'll never go back to adhesive lint rollers or static brushes after risking $6 on it.
Even on freshly vacuumed rugs that seem hair and dust-free, it rolls it up by the rope:
The only caveat is that you'll still need to pick all the fuzz off it, either a vacuum or your bare hands, as you work.
Don't wet it, except to clean it. Just rub the sponge lightly on furniture or floors and it all comes up, reminding one that that no matter how clean one thinks one's house is, so long as it has carpet, curtains or dogs in it, it's actually a floating, roiling ocean of hair, dander, and billions of particles of shit, settling to form an invisible veil of filth on everything and everyone within.
Gonzo Pet Hair Lifter [Amazon link]