What might happen to you if circuit breakers were not installed in a circuit in a house?

Any overload might result in a fire since there isn't a standard method of limiting current without the circuit breakers.

Circuit breakers cannot and do not protect a person from being electrocuted (a ground fault interrupter GFI breaker can, but that is a different device that is only required on outlets near water like sinks and showers). The ONLY reason they are there is to prevent a short circuit from causing the wiring to melt and catch the house on fire!!! They are thus a requirement of both the electrical code and the fire code. What is likely to happen is if that circuit was connected by a licensed electrician he would lose his license and probably be criminally prosecuted and you could also sue him for damages in civil court. If not installed by a licensed electrician when (not if) your house eventually burned down and the fire investigation was done, your insurance would refuse to pay any claims for fire damage as the building failed to meet code and that failure was the direct cause of the fire.

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The electrical code calls for an over current device every time there is a conductor size change. On a 100 amp service, the conductor size is a #3, with an insulation factor of 90 degrees C it is rated for 115 amps. This is the same ampacity rating of the distribution panel. You can see that by installing a household circuit with a #14 conductor which is only rated at 15 amps, the only overload protection for that wire will be the 100 amp main breaker ahead of it. Drawing 100 amps on a #14 wire will heat the wire up to a point where the insulation will melt off the wire. If the wire grounds out sparks will fly and this action could ignite surrounding combustible material. To answer the question, if you are not standing physically close to the panel nothing will happen to you but you might not have a house left to live in.