That's right! We would freeze to death, we would eventually not have any food to eat and Earth along with all the other planets would go flying off in space. It would be total havoc and chaos in our solar system.
Here is an amazing video courtesy from YouTube about what will happen if the sun disappeared.
Here are some very interesting facts:
Initially, a cloud destined to become a star will be roughly spherical. The cloud will almost certainly have a slight rotation, simply because of random gas motions in the cloud as it started contracting. As the cloud contracts, its rotation will speed up, causing the cloud to become disk-shaped. The cloud is still far larger than our solar system, and its outer reaches very thin. Most of the mass of the cloud falls to the center, adding energy to the center and heating it up. The center of the cloud becomes a protostar, emitting mostly infrared radiation. Finally the temperatures and pressures within the star reach the point where nuclear reactions begin, and the star "turns on". Matter in the surrounding disk may accrete to form planets, or, if the condensations are massive enough, companion stars.
All living beings on earth needs the sun to survive. It provides most of the energy on earth for us to survive. Plants also need the energy from the sun for creating their own food through photosynthesis and in turn manufactures oxygen for us to breath.
Here are some more links if you want to read more about the sun. It is an amazing topic to explore so I suggest you do some more research about this on your own:
https://www.uwgb.edu/dutchs/AstronNotes/STARS.HTM
http://space-facts.com/the-sun/
https://www.space.com/58-the-sun-formation-facts-and-characteristics.html
http://www.sciencekids.co.nz/sciencefacts/space/sun.html