"Why would anyone bother looking after them?"
-Ron Weasley, PA8
A ten-inch, toothless brown worm which eats vegetation, especially lettuce.
Hagrid, after losing his nerve with the hippogriff debacle, had his third year students raise these for a semester, which was completely pointless as they prefer to be left alone and to do nothing (PA6, FB). They live in damp places such as ditches (FB).
In his retirement, Professor Kettleburn kept a number of Flobberworms at his home in Hogsmeade, and, being physically unable to partake in the Battle of Hogwarts, he did his part by throwing them all at passing Death Eaters through his attic skylight. It was not very effective, but his effort was appreciated (Pm).
The information regarding Professor Kettleburn and the Battle of Hogwarts comes from the new Pottermore ebook.