  A plethora of natural, artificial and social systems exist which do not
belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the
standard additive entropy $S_{BG}$ and its associated exponential BG factor.
Frequent behaviors in such complex systems have been shown to be closely
related to $q$-statistics instead, based on the nonadditive entropy $S_q$ (with
$S_1=S_{BG}$), and its associated $q$-exponential factor which generalizes the
usual BG one. In fact, a wide range of phenomena of quite different nature
exist which can be described and, in the simplest cases, understood through
analytic (and explicit) functions and probability distributions which exhibit
some universal features. Universality classes are concomitantly observed which
can be characterized through indices such as $q$. We will exhibit here some
such cases, namely concerning the distribution of inter-occurrence (or
inter-event) times in the areas of finance, earthquakes and genomes.
