If the sun simply vanished the earth (with moon on tow) would follow Newton and continue in a straight line. Unlikely anyone would notice instantly - the earth's gravity at it's surface vastly exceeds the sun's influence but it would certainly mess up the tides. Sailors would know something is up but not what. It's conceivable that there would be widespread tsunamis depending on the earth's rotation relative to the sun when it went poof and the day's tides relaxed.
People on the day side would start to panic 8 minutes later when the lights go out, people on the night side would have a few more hours of peace and quiet.
After that, we can look forward to steady cooling. The deep ocean probably won't freeze for millennia but primary production will stop, the food chain will collapse, and everything on the surface will likely expire after a few months. Well stocked survivalists might last a year depending on their fuel reserves. (this is purely guesswork on my part)