Without the sun, all life on Earth except for deep sea microbes would die. Earth would cool to minus 100 degrees Fahrenheit within one year, plants would be unable to photosynthesize and gravity would no longer keep the Earth in orbit.
Surface freezing of the ocean would likely insulate deeper waters from freezing solid, which would allow deep sea bacteria to survive. Geothermal heating from Earth's core would continue, providing heat and chemical nutrition to these microbes. Because plants require sunlight for photosynthesis, they would die off; this would trigger the collapse of the food chain. Animals would die off due to either cold or starvation.
Earth would also lose some of its protection against interstellar radiation; solar winds and the sun's magnetic field generate a protective sheath called the heliosphere. The heliosphere blocks 90 percent of cosmic radiation originating outside the solar system, and without it this radiation would reach the Earth.
The sun's gravity keeps the solar system in its current orbit. The decay of every orbit in the solar system would put the Earth at risk for collision with asteroids, comets and other planets. Eventually, every planet in the solar system would be ejected into interstellar space.