What would happen if the moon exploded?

There would be a loud BANG and we would have no more moon. There, simple.

Actually, a lot more would happen than a loud noise and the song "Moon River" becoming obsolete.

The moon effects the tides as we know them, without the tides the oceans would become giant stagnant pools, incapable of sustaining the life they currently do.

Most importantly, the moon keeps the earth titles on its axis. Think of it like someone spinning around holding a heavy bag of shopping. The bag would fly out at an angle and the spinning person would lean back at an angle. Without the bag, someone spinning around would do so perfectly vertically. Without the moon, the earth would spin in the same manner. We would lose the seasons and the earth would become divided into three sections, two incredibly cold, inhospitible frozen wastelands roughly covering the top and bottom thirds, and a scorching desert covering the middle strip.

This is because the tilt of the earth makes a location in its surface follow an arc as it rotates, making sure it gets the right amount of heat and shade to sustain life.

There would be thin sections of land that were positioned just right so that the temperature neither froze or fried you, but the wind patterns would be so altered that harsh storms would constantly rage.

It's just occurred to me that "What would happen if the moon exploded?" sounds like someone Jeremy Clarkson would say just before cutting away to one of Top Gear's more bizarre experiments. So, please, don't forward this to him.