I'm one of those players who have benefited from the Insufficient Mating Material rule. I was playing in a national open tournament, and had just cleared the 2-minute mark on my clock before the Sudden Death time control.
My opponent had been whittled down to a bare king, but my pieces and pawns were not coordinated enough (read: too cluttered and disorganized) to grind out a midboard mate or wedge him over to the edge of the board reliably in the time remaining.
So, I hailed a TD, and reported my intention to claim a draw based on the above rule. The TD looked the position over, saw that my opponent had no chance of winning without the clock, and ruled a draw. That saved me a 1/2 point.
The FIDE rules state (Article 9.6):
"The game is drawn when a position is reached from which a checkmate cannot occur by any possible series of legal moves, even with the most unskilled play. This immediately ends the game."
I recall hearing that GM Josh Friedel attempted to claim a draw on this basis once in a game he was playing in Europe, but the FIDE rule allowed for a helpmate which was possible with the material his opponent still had (he had two knights). Friedel was ordered to play on, with a time penalty for a denied draw claim. Unsurprisingly, he lost on time.
By the way the USCF rules differ from FIDE's: It is necessary for the player with the inferior material to be able to force mate. It can't be only available through a miracle or the assistance of the opponent, and depends on the player's ability. The arbiter has discretion regarding the complexity of the mate and whether an average player of the appropriate class would be able to execute the mate. This is much more forgiving than FIDE's definition.
For those of us who aren't familiar with the theoretical draws based on material, a nice summary is presented by the E4 Email Chess Club.