If you're taking the violin in and out of the house, you'll definitely need a case to keep the instrument safe from the weather and the bangs and dings that can occur when you're carrying it around. If the violin is dinged, it hurts the look of the instrument and can cause it to go out of tune. Never leave your violin in the car, as excessive heat or cold can damage the instrument.
When you're at home, the violin case protects the instrument from dust. In addition, households with children or pets may find it safer to store the violin in a case to keep the instrument out of harm's way. In homes without children or pets, you can safely hang the violin on the wall (or another safe location) as long as it is regularly dusted and safe from any possible water damage.