It is believed that most invertebrates, including insects, are unable to feel the sensations we call "pain." Fundamentally, they lack a central nervous system, which we think is prerequisite for pain sensation. They also don't respond to damaging stimuli in a manner that would suggest they feel pain. However, we cannot experience what they "feel," nor can they tell us. All we can do is assume that if other species feel pain they must have the same equipment and show the same responses as us. Unfortunately, most conclusions that animals don't feel pain have been used to justify and excuse some pretty barbaric behavior on the part of humans. Or...Is it barbaric if the subject really doesn't feel pain (or fear)? These are philosophical questions that I'll leave to someone else.
There's a nice essay on the subject of whether animals can feel pain at http://www.wellcome.ac.uk/en/pain/microsite/culture2.html. There's also an interesting table at http://www-phil.tamu.edu/~gary/revolution/pain.html that shows which animals have which characteristics.