I use a similar method to amelinda's quite often, but it's a bit more amusing. I usually use it to decide such patently irrelevant matters as which glass of orange juice should go to my girlfriend and which should glass should go to me. The (quite simple) system goes as follows:

1. Alice and Bob have a decision to make, between a virtually limitless number of options. We'll say they have three: they're deciding whether to go to the park, the river, or the mall.
2. Alice assigns three unrelated words to each of the different options. The park becomes "sneeze", the river becomes "freckle", and the mall becomes "tiger". Alice does not inform Bob of these assignments.
3. Alice then asks, "Tiger, freckle, or sneeze?"
4. Bob picks whichever one happens to strike his fancy, Alice informs him of the corresponding option, and a decision is made.
While this method is arguably not completely random, as Alice could have a subconscious wish to go to the mall, and, knowing that Bob likes cats, she would therefore subconsciously assign the value "tiger" to the "mall" option. However, the system works beautifully and amusingly when the decision has no significant import.