General synonyms:
* Boasted
* Showed off
* Gloated
* Vaunted
* Lauded
* Touted
* Extolled
* Puffed up
* Showed off
More specific synonyms:
* If it's about achievements:
* Brag
* Swagger
* Fanfaroned
* If it's about possessions:
* Showed off
* Flaunted
* Paraded
* If it's about appearance:
* Strutted
* Prance
* Postured
Less formal synonyms:
* Bigged up
* Blowed their own trumpet
* Went on about
* Had a go at
* Made a fuss about
The best synonym for "bragged" will depend on the specific context and the tone you want to convey.