Loud eaters pose a more difficult problem because asking them to make less noise means you are commenting on something very personal -- they way they eat, which many contend is something we have little control over, like the way we talk or the way we walk. So if you sit next to someone who chomps, slurps, and slaps their gum all over, be careful when asking them to change their behavior. Do it tactfully. Take a broader approach and tell them how it is beneficial in many ways to eat one's lunch away from their desk. Beneficial in many ways for everyone.
Funny enough, there's even a Facebook page dedicated to loud eaters.