We deal with the existence of positive bound state solutions for a class of
stationary nonlinear Schr�dinger equations of the form $$ -\varepsilon^2\Delta u
+ V(x) u = K(x) u^p,\qquad x\in\mathbb{R}^N, $ where $V, K$ are positive
continuous functions and $p > 1$ is subcritical, in a framework which may
exclude the existence of ground states. Namely, the potential $V$ is allowed to
vanish at infinity and the competing function $K$ does not have to be bounded.
In the \emph{semi-classical limit}, i.e. for $\varepsilon\sim 0$, we prove the
existence of bound state solutions localized around local minimum points of the
auxiliary function $\mathcal{A} = V^\theta K^{-\frac{2}{p-1}}$, where
$\theta=(p+1)/(p-1)-N/2$. A special attention is devoted to the qualitative
properties of these solutions as $\varepsilon$ goes to zero.