What is the path of the nerve impulse that travels through your body from stimulus to response?

Sensory information is gathered by receptors throughout the human body.  Sensory receptors are stimulated by stimuli coming from the external environment as well as the environment inside of the body.  In this example, let's assume that touch is the stimulus.  

Pressure on receptors in the skin like Meissner's corpuscles and Pacinian corpuscles can deform the capsule covering the dendrites of the sensory neurons that they encapsulate.  This will open mechanically-gated channels within the dendrites of the sensory neurons and create a graded potential as sodium ions enter the neuron in that region.  If enough pressure is applied, enough channels will open and enough sodium will enter to bring the voltage difference across the neuron's membrane to the threshold (-55mV from the resting membrane potential of -70mV).  Because sodium ions are positively charged, when they enter the cell, the charge on the membrane becomes more positive.  This reaching of threshold allows an action potential to be sent through the sensory neuron.  This sensory neuron is the 1st order neuron in the pathway.

The 1st order sensory neuron or neurons will synapse with the second order neuron or neurons in the spinal cord or brain stem.  At this point, decussation or crossing over from the right side of the body to the left (or vice versa) will occur.  This is why it is said that the left side of the body is controlled by the right side of the brain (and vice versa).  This frequently occurs in the medulla oblongata.  

The 2nd order neuron then ascends to the thalamus of the brain and synapses with the third order neuron which carries an action potential to the primary somatosensory cortex of the cerebrum.

Integration and processing of the incoming sensory information occurs in the cortex and then motor information that is sent to the effectors (in this case skeletal muscles).  Assuming that a direct pathway is used, the upper motor neuron will originate in the primary motor cortex of the cerebrum and if it is stimulated enough to reach threshold (this has to happen every time in order for a neuron to generate an action potential), then an action potential will be sent down toward the lower motor neuron.  The upper motor neuron typically synapses with the lower motor neuron in the spinal cord after decussation. The lower motor neuron then carries the action potential to the effector.  

In this case the effector is a skeletal muscle.  The action potential from the lower motor neuron will cause the release of acetylcholine in the synaptic cleft between the neuron and the muscle fibers.  The acetylcholine will cause the opening of ligand-gated sodium channels at the motor end plate and this will eventually lead to contraction of the muscle.  This contraction could cause a person to move his or her arm in response to the touch (the original stimulus).