Maybe!
The answer depends on what other pieces are on the board. If your opponent only has a king and you have a King and bishop, then it is a draw. if you have a K and B, and your opponent has a K, N and P then you win, because it is possible for legal moves to put him in checkmate. (even if he would not make those moves)
Here is the official rule:
Law 6.10 of the FIDE Laws of Chess states that: "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, even with the most unskilled counterplay." As an example, a player with king and bishop can claim a win on time against an opponent with king and knight, whose clock flag has fallen, because a mating position can be produced by a series of legal moves.
There are other ways to call a draw before this happens.
article 10 of the FIDE laws of chess states that when a player has less than two minutes left on their clock during a rapid play finish (the end of a game when all remaining moves must be completed within a limited amount of time), they may claim a draw if their opponent is not attempting to win the game by "normal means" or cannot win the game by "normal means".
For further explaination, see diagram at bottom of this page:
http://en.wikipedia.org/wiki/Draw_(chess)
EDIT: Adding link to FIDE Handbook (section E.1 is laws of chess)
http://www.fide.com/official/handbook.asp?level=ogl
EDIT:
Lots of false information here:
In the above scenario, if your opponent has a K+N, and you have K+B and his time ran out before you, then you WIN You must have enough pieces to have a possible mate on the board, but you do not need enough pieces to force mate.
So if you have a K+B and your opponent has a K+N,
Then if the Opponent K is on H8, Opponent N is on H7, Your K is on F7, and your B is on G7 it is MATE and it is possible to get into that position with legal moves; therefore you win if your opponent ran out of time. (see the wikipedia page I posted)