Game drawn without enough material to mate even if opponent runs out of time? Does this apply to OTB chess as well?  I was playing an online game on FICS and my opponent ran out of time, but I did not have enough material to mate, so the game was drawn.
Yes.
This is an official rule, see Article 6: The chess clock of the FIDE rules handbook (E.I.01A. Laws of Chess). Section 6.9 goes :

Except [in checkmate and stalemate cases, mutually agreed draws and resigned games,] if a player does not complete the prescribed number of moves in the allotted time, the game is lost by the player.
However, the game is drawn, if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.