Are there any (pairs of) simple distributions that give rise to a power law ratio? If I recall correctly, for $X$, $Y$ normally distributed, the ratio $X/Y$ is Cauchy-distributed. This is sort of like a power law, but isn't quite. So:

Are there any simple distributions for two RVs $X$, $Y$ s.t the ratio
  is really power-law distributed (at least in some regime)?

 A: According to Wikipedia, if $X\sim\mathrm{Exponential}(\lambda)$ and $Y\sim\Gamma (n, \frac{1}{\lambda})$, then $\frac{X}{Y}\sim$Pareto$(1,n)$.
NOTE: Wikipedia is not quite right on this one.  See Dilip's response.
A: As noted here, Wikipedia's answer to the question posed by the OP is not quite correct.  If $X$ is a Gamma random variable with parameters $(n,1)$ and $Y$ is an exponential random variable with parameter $1$ and $X$ and $Y$ are independent random variables, then $Y/X$ is not a Pareto random variable, 
but $Z = Y/X + 1$ is:
$$P\{Z > z\} = P\{Y/X + 1 > z\} = z^{-n}~ \text{for}~ z > 1.$$
A common scale parameter $\lambda$ could be included in both variables, but since we are looking at ratios, the scale parameter cancels out, and it is convenient to set $\lambda = 1$.
Suppose that $X$ denotes the time of the $n$-th arrival after $t = 0$ in a Poisson process with arrival rate $1$.  Then $X$ is a Gamma random variable with parameters $(n,1)$.  Let $Y$ denote the additional waiting time for the $(n+1)$-th arrival.  Then, $Y$ is an exponential random variable with parameter $1$ and is independent of $X$.  Thus, we have the situation described in the previous paragraph.  But notice that the $(n+1)$-th 
arrival time is just $W = Y + X$, and $Z = Y/X + 1 = (Y+X)/X = W/X$ is thus the ratio of the $(n+1)$-th and $n$-th arrival times, and is a Pareto random variable.  Naturally 
$Z > 1$.

In summary, if $W$ and $X$ are the $(n+1)$-th and $n$-th arrival times in a (homogeneous) Poisson process, then $W/X$ is a Pareto $(1,n)$ random variable:  $P\{W/X > a\} = a^{-n}$ for $a > 1$.

