Normal events - controls are specified in a particular order, fastest time wins.
Score events - visit as many controls as possible within a given time in any sequence you like. Control points have different values depending on distance and degree of difficulty, penalties for exceeding the time allowed.
Night events - like a normal event but it's dark!!! (you use a head torch to see!!)
Relay events - a team event
Long 'O' or Mountain 'O' - Longer distance courses in hilly or mountainous areas - greater distances between controls.
Mountain marathon - as above but you carry overnight equipment and food.