Most of the time I use the well worn, round synthetic sponge you see here. Since its old and worn I use to clean and dampen my bat. My intention is to then grab a nicer sponge to use while throwing but that doesn't always happen. Habit brings my hand back to the old sponge. It still works well so why not. You see I have a Michael Sherrill Mudtools sponge. I love my Michael Sherrill Mudtools ribs, and I love this sponge. The shape fits into my hand really well, it distributes water almost as well as a natural sponge but they cost a bit more than the round sponges and when the edge starts to wear it's about done for throwing. I can't afford to be replacing more expensive sponges very often so I don't. This is the blue version, they now make an orange sponge but I've not tried that yet. Have you?
I use the flatter natural sponge and the elephant ear sponge to throw also. Natural sponges hold and absorb water very well. They are great for throwing and feel good in the hand. They also hold up really well. I love the flat one for detail cleaning in tight spots like handle attachments. It's a must have.
The larger sponges are used for cleaning the contrasting slip from a pot during the Mishima process. I use them because they mop off the slip really well. I assume because of the way natural sponges handle water.
If you've read this entire article you might just be a potter, who else would read four paragraphs about sponges? Hehe. Whether you're a potter or not you should check out the other potters at Mudcolony.