I have experienced two instances of game crashes while playing Brink.
In both instances (so far), the game seemed to be in the process of loading prior to causing the game (and the Xbox) to be indefinitely unresponsive.
The first instance was during a map pre-loading screen (i.e. when the captions are present on the black screen which features the stylized art specific to the particular map while the map-specific story audio plays prior to the cut-scene and prior to the appearance of the ~‘Press Any Button to Start Game’ prompt)
The second instance was after exiting a game and attempting to return to the menu. Normally, this would take me to the character modification menu featuring options such as ‘Appearance’, ‘Weapons’, ‘Abilities’, ‘Character Selection’, etc. Prior to the crash, the avatar of my character did not load properly on the screen.
In both instances, Brink was in the process of loading something when the game froze.