General synonyms:
* Courageous
* Bold
* Valiant
* Daring
* Fearless
* Intrepid
* Audacious
* Gallant
* Heroic
* Stouthearted
* Spirited
* Resolute
* Undaunted
* Unflinching
* Mettle
* Grit
More specific synonyms:
* For facing danger: dauntless, fearless, intrepid, undaunted
* For showing strength of character: resolute, stalwart, tenacious, strong-willed
* For being willing to take risks: adventurous, bold, daring, audacious
* For being respectful and chivalrous: gallant, noble
More informal synonyms:
* Gutsy
* Tough
* Game
* Spunky
The best synonym for "brave" will depend on the specific situation and the tone you want to convey.