žderati

1. colloq. derog. (of food) to stuff one's face; to gorge; to pig out
   Ne žderi toliko, posle ćeš imati muke. — Don't stuff your face like that, you'll feel sick later.
   Ceo dan samo ždere čips ispred televizora. — All day he just gorges on crisps in front of the TV.
2. colloq. (of a car, expenses) to guzzle; to eat up
   Ovaj stari auto ždere benzin kao lud. — This old car guzzles petrol like crazy.
3. colloq. (žderati se, of worrying) to fret; to torment oneself; to beat oneself up
   Ne žderi se zbog toga, sve će biti u redu. — Don't beat yourself up over it, everything will be fine.
   Ona se ždere što nije položila ispit. — She's beating herself up over failing the exam.
4. colloq. (of conscience, jealousy) to eat at; to gnaw at; to torment
   Ždere ga savest što joj nije rekao istinu. — His conscience is eating at him for not telling her the truth.
   Ljubomora je ždere već mesecima. — Jealousy has been gnawing at her for months.

A rude word; the neutral verb is jesti.