This depends on where in the country you live. In general, the most likely time would be between the hours of about 3pm and 9pm, since this is generally when thunderstorms are most likely. But in the deep south, tornadoes often strike at night while people are in bed, which is why---in the old days, before warning sirens were installed---the numbers of tornado deaths and injuries were historically higher in states like Alabama, Mississippi and Kentucky.
The reason for this daily shift from afternoon twisters in Texas, Oklahoma and Kansas to more night time outbreaks farther east involves a phenomena called the dry line. On many days in the late spring and summer, an area of hot, dry air builds up in the southwestern U.S. and spills east toward the more moist air along the Gulf Coast. This clash between the dryer, more dense air and the lighter, more buoyant air is an excellent storm formation set-up. As the sun rises, the dry, heavier air expands and pushes toward the east. It takes until nightfall for it to reach the southern states, which is why storms are more common then. Overnight, the dry line recedes back into Texas to begin the cycle anew.
---David Murphy
