These are great for a number of reasons. They have cloth on the outside (both sides, they are reversible) so they feel nice to touch and can be used to wipe the baby's face. But, they have a waterproof lining in the center which means that even if your kid dumps an entire spoonful of soup on herself, her shirt will remain intact. And, unlike their plastic counterparts, these are machine washable. This means cleaning the bibs is no extra work (you do laundry every other day anyway, right?). The absorptive fabric/waterproof combo also comes in handy for that charming month or two in your baby's life when rivers of drool are constantly coming out of their mouths.
Now I have a second baby who, wonder of wonders, is a totally different child. We haven't started feeding him solids yet. However, we've already had to break out the bibs due to the massive quantity of spit up he produces. And let me tell you, despite the number of novelty bibs in my drawer growing with the number of children, I pretty much always still reach for the green sprouts.