Are all action potentials the same shape and amplitude when graphed with respect to time?
Short answer
Action potentials differ in shape between neuronal cell types, and action potentials may even change shapes during action potential propagation within one and the same axon. 

Background



  Once an action potential is sent from a given neuron down the axon, does the shape and amplitude remain constant as it is propagated?



Although the textbooks will typically say action potentials are transmitted without their amplitude being changed this claim is theoretically virtually impossible due to the many variables encountered in and around the axon. For example, axons in the sciatic nerve may extend to a meter and it is virtually impossible to keep the exact conditions along that length exactly identical. The amplitude of the action potential is mainly dependent on the influx of Na+. Slight variations in membrane potential, concentration of sodium, or channel (subtype) densities may therefore change the amplitude. In addition, temperature affects action potential amplitude (Hodgkin &amp; Katz, 1949) and slight temperature differences along long axons may therefore be expected to alter amplitude. Likewise, shape may alter as well. For example, glutamate released alongside axons of hippocampal pyramidal neurons results in widening of action potentials (Sasaki et al., 2011).   



  Do all action potentials have the same amplitude and shape? 



Therefore, given the answer under question 1 no, they do not have to. Even a propagated action potential in a given axon may change amplitude and shape, as said. Most notably, different neuronal types may in fact be classified according to their action potential morphology, such as the various neuronal types in the dorsal root ganglia of the spine that can be differentiated based on their duration (Villiere &amp; McLachlan, 1996).  

References
 - Hodgkin &amp; Katz, J Physiol; 109: 240–9
 - Sasaki et al., Science 2011; 331: 599-601
 - Villiere &amp; McLachlan, J Physiol 1996; 76: 1924-41