I recently saw a game where a player tried to save the ball from going out of bounds, and in the process scored in the wrong hoop. This player was saving the ball from beyond the three-point line.
Should this have been awarded with three points? The score in the game only increased by 2, but I'm not sure if there is a rule which accounts for this circumstance.
The FIBA rules have defined how points are awarded for an own goal.
Article 16.2.2
If a player accidentally scores a field goal in his team’s basket, the goal counts 2 points and shall be recorded as having been scored by the captain of the opposing team on the playing court.
NCAA Men's Basketball rules are a bit more detailed in this regard (emphasis mine).
Rule 5 Article 4
When a player scores a field goal in the opponent’s basket, it shall count two points for the opponent regardless of the location on the playing court from where it was released. Such a field goal shall not be credited to a player in the scorebook but shall be indicated with a footnote.
So it looks like an own goal is worth two points only, irrespective of the location from where the ball was released.
PS: NCAA uses the term 'opponent's basket' while FIBA uses the term 'his team's basket'. This is down to the definition of own and opponent's basket which is contradictory for both. For FIBA, refer Rule 1 Article 1.2 and for NCAA, refer Rule 1 Section 1 Article 2.
