Also a three way light may always have power in the box depending on switch layout. Light fixture troubleshooting question.

How Long Do Gfci Outlets Last Homelectrical Com
If light switch is off is there still power. When the switch is on you get full voltage but when the switch is off current flows from hot through the switch and into the high resistance ground fault. The switch actually breaks power in the hot or black wire between the circuit breaker and the light. The switch does not work. That doesnt mean you should do it. I have power coming off of one lead and when i cross the leads the light still wont work. One possibility is that the switch is wired on the neutral side and there is a ground fault between the switch and the outlet.
Very common a big misconception with deadly results. However there is very little energy transferred so the phantom voltage is usually not dangerous because it can produce almost no current. Just to recap a phantom voltage is where a wire from a switch to a light or outlet runs next to a permanently live wire when the switch is off the ac voltage in the other wire can induce a voltage in the switched off wire. I recently had a dimmer switch go out on me and i replaced it with a regular switch. See the details below second and of a greater concern to us when the outlet is off a lamp plugged into it turns off with the switch there is still power going through the outlet. That is why when dyis want to add a receptacle next to a switch it does not work.
Last night the light just came on by itself. If there is a single switch in the circuit then yes there should be no electricity present. The light and switch single pole have been in operation for 15 years. Test the circuit again by putting your test leads on the two screws that attach the wires to the. If the light is off no power there a very standard configuration is power to the light then a switch leg to the switch. It is generally safer to turn off the entire circuit in case someone comes in and flips the switch to give you some light to see what you are doing.
As i stated i changed the switch but the light stays on constantly even without being connected to the switch as long as the breaker is onthe box has three set of wires blackwhiteground from the fixture a blackwhiteground and a blackredwhiteground.