General synonyms:
* Consume
* Ingest
* Devour
* Gobble
* Munch
* Nibble
* Chew
* Swallow
Formal synonyms:
* Partake
* Feast
* Dine
* Graze
* Consume
Informal synonyms:
* Chow down
* Stuff oneself
* Gorge
* Pig out
* Noshe
Synonyms for specific actions:
* To eat quickly: Bolt down, scarf down, gobble up
* To eat a lot: Fill oneself up, stuff oneself
* To eat delicately: Nibble, pick at
* To eat without being hungry: Snack, graze
The best synonym for "eat" will depend on the specific situation you're describing.