Of course they feel pain. Pain is a protective sensation so that the creature can avoid further damage if possible. If you lay your hand on a hot burner the pain causes you to jerk away before further burning occurs. If you have a broken limb pain causes you to protect it.

Having said that, wild animals are a lot tougher than us. They live there whole lives exposed to the elements, fighting to survive. That alone would make them more tolerent of pain without considering phyical traits like the nervous system.

Think on this, there are very few quiet, peaceful deaths in the wild. Animals starve, freeze to death, are ripped apart and eaten by other animals. Its my way of thinking that a well placed bullet is one of the quickest and cleanest deaths a wild animal could expect.