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Backgammon Variants 
Have you ever wished, after rolling the worst possible number, that you could just pick up your dice and roll again? Or wouldn't it be fun to make your opponent take back his roll after he gets the one pair of numbers that allow him to enter and escape his lone back checker? That's the idea behind Roll-Over.
Roll-over: Once per game, each player has the option of either rolling again if he doesn't like the numbers he's thrown, or asking the opponent to roll his dice again. You may decide to reroll your own dice any time before you pick them up. So you can try out various plays before deciding what to do. Similarly, you can wait until your opponent completes his turn before asking him to roll over. When a player says "roll-over," the roll is cancelled and any moved checkers are restored. The player whose roll was cancelled then rolls the dice again. At this point, if the opponent still has his roll-over option, he can cancel the reroll and the dice are rolled yet again. So it is possible in rare situations for the dice to be rolled three times in one turn. The roll-over rule brings a another decision to every roll of the game. In some games you will use this option early, in other games very late, and in some games not at all. Roll-over marker. It is a good idea for players to start off the game with a special marker denoting their "roll-over". When a player uses his roll-over, he sacrifices the marker so there is no dispute later in the game about whether or not the roll-ver was used. Doubling. The doubling cube is used just as in regular backgammon. Note that once a player has rolled the dice, he may not double that turn. Even if he rolls over, he must wait until his next turn to offer the cube.
References
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Backgammon Galore : Variants