Proton NMR spectrum of aminocaproic acid
The N+1 rule, in its ideal form, assumes that for multiplets arising from $\mathrm{^3J}$ couplings between neighbouring $\ce{CH_2}$ groups,  


shifts for the spins within a $\ce{CH_2}$ group are identical
all couplings between spins in two different groups are identical


While condition 1 usually holds for substituted alkanes of the form $\ce{A-(CH_2)_n-B}$, condition 2  does not. This leads to the title "Is the n+1 rule ever obeyed?" in a section of a textbook [1], like a cry of despair. The text elaborates: 


  At other times, when there is a large difference between $\mathrm{^3J_{AB}}$ and
  $\mathrm{^3J_{BC}}$, distinct peaks, more than five in number, can be seen.
  Deviations of this type are most common in a chain of the type 
  $\ce{X-(CH_2)_3-Y}$, where X and Y are widely different in character.


So, the exception is actually closer to the rule, and that is because true magnetic (unlike chemical) equivalence is relatively rare. 

[1] Pavia, Lampman and Kriz, Introduction to Spectroscopy, 2nd Ed., Saunders Publishing