When is it appropriate for the arbiter to reduce a player's time? According to the FIDE Laws of Chess:


  12.9 Options available to the arbiter concerning penalties:
  
  12.9.1 warning,
  
  12.9.2 increasing the remaining time of the opponent,
  
  12.9.3 reducing the remaining time of the offending player,
  
  12.9.4 increasing the points scored in the game by the opponent to the maximum available for that game,
  
  12.9.5 reducing the points scored in the game by the offending person,
  
  12.9.6 declaring the game to be lost by the offending player (the arbiter shall also decide the opponent’s score),
  
  12.9.7 a fine announced in advance,
  
  12.9.8 exclusion from one or more rounds,
  
  12.9.9 expulsion from the competition.


In a FIDE rated competition (or one in which the FIDE laws apply) when is it appropriate to apply a time reduction as a penalty?

I know of one such, which I will give as a separate answer. I would like to know if there are more.
According to the FIDE Laws of Chess:


  8.1.1 In the course of play each player is required to record his own moves and those of his opponent in the correct manner, move after
  move, as clearly and legibly as possible, in the algebraic notation
  (Appendix C), on the ‘scoresheet’ prescribed for the competition.


In Israel a lot of the leagues play on a Saturday between 10 am 2 or 3 pm. Obviously all of the people who play have religious beliefs which are consistent with this, unlike Samuel Reshevsky who refused to play on the Sabbath. There are, though, a very small number of players who's beliefs allow them to play chess on the Sabbath but not write the moves down because that resembles the work of a scribe, could therefore be construed as work, and is there fore forbidden to them.

In this situation it has been agreed with the the arbiters overseeing the competition that these players may be excused the requirements of article 8.1.1 but must suffer a time penalty of 10 minutes. So, in a 90+30 game (all moves in 90 minutes with a 30 second increment from move 1) they start with 80 minutes on the clock plus increment instead of 90.

This is actually mentioned in article 8.1.6:


  8.1.6 If a player is unable to keep score, an assistant, who must be acceptable to the arbiter, may be provided by the player to write the
  moves. His clock shall be adjusted by the arbiter in an equitable
  way. This adjustment of the clock shall not apply to a player with a
  disability.


It is worth noting that players with disabilities are not subject to this time penalty. 

I've applied this principle in mid-week tournaments where a player has refused from move 1 to write the moves down and also refused to give an explanation. Such a solution is obviously preferable to trying to coerce the player or to exclude the player from the competition, both of which would be highly undesirable.