The old saying goes "You only miss it, when it's gone" and it couldn't be more right. There are things we see, use, and/or depend on every day that we sometimes take for granted; the sun for example. The thought of a world without the sun probably makes you think of the end of the world or mass chaos, but the truth actually may surprise you.
So let's just say the sun just disappeared, not exploded, not burnt out, just vanished, what would happen. Well to start we wouldn't even know the sun was gone at first. It takes approximately 8 minutes and 20 seconds for light to travel from the sun to the Earth. () It's safe to assume that by the time we found out it was gone, confusion and panic would ensue. Not only that but at the moment in time in which we discovered the sun was gone, we would lose its gravitational influence, "and Earth would fly out in a straight line tangent to where ever it was in its orbit" () This is because gravitational force propagates in waves moving at the speed of light.
So now poor, little Earth is hurtling through space, in a perpetual night, but we wouldn't be completely in the dark. We would still have the rest of the galaxy producing light. In 2004, a scientist () calculated that the Milky Way alone produces about 1/300th of a full Moon. It's not much but it's enough to help us see around. Not only that but we would still have fossil fuels and other energy producing techniques, excluding solar obviously, to keep the Earth lit up for a while, just like any other night.
Another crucial aspect of the sun is photosynthesis. For those that don't know, this is the process in which plants use sunlight to turn water and CO2 (Carbon-dioxide) into sugars and Oxygen. About 99.9% of the natural productivity of the Earth is dependent on photosynthesis, which in turn is dependent of the sun. But don't let this bring you down because the Earth will still stay strong, at least for a while.