In reply to Maddie
belay device attached incorrectly
belay device set up incorrectly
belay device jammed (hair or fingers stuck in ATC etc)
climber stuck in bolt hanger / clipped quickdraw onto themselves
climber at height with incorrect knot
climber at height with incorrect harness
soloing and stuck
loop of rope stuck around hold and climber above
climber has traversed off their own line
Step One in a rescue scenario is always make the climber safe.