General Courage:
* Bold
* Courageous
* Daring
* Fearless
* Intrepid
* Valiant
* Gallant
* Heroic
* Audacious
* Spirited
* Resolute
* Stalwart
Facing Fear:
* Undaunted
* Unflinching
* Unwavering
* Gritty
* Tough
* Tenacious
Facing Danger:
* Adventurous
* Rash (can have a negative connotation)
* Reckless (can have a negative connotation)
Facing Difficult Situations:
* Strong-willed
* Determined
* Unyielding
* Resilient
* Persistent
* Unflappable
Specific to a Particular Situation:
* Noble (for brave actions for a good cause)
* Selfless (for actions putting others before oneself)
* Generous (for actions that are kind and brave)
* Magnanimous (for actions that are forgiving and brave)
The best word to use will depend on the specific context and the nuance you want to convey.