I have two boys that are blanket lovers. They have singled out one blanket that is their "one and only." It MUST be there when they nap, when they play, when they eat......we had to draw the line when it came to bath time. ;)
They are not THAT bad, but pretty close. So when you use a blanket THAT much it can look like this pretty dang quick.
I knew if I threw the blanket out, I would not cease to hear the cries of withdrawal. So I decided to have them pick out fabric that they liked and THEY helped me cover the old blanket with new fabric. This way I was not REALLY throwing out the blanket, but making it look "cooler". Having them help me, made them more excited to have it done. So now the blankets look nice and my kids are not mad that the "old" blanket is gone.
I imagine you could do this with a stuffed animal as well, but it may take more work.