  Let $G$ be an edge-colored graph on $n$ vertices. The minimum color degree of
$G$, denoted by $\delta^c(G)$, is defined as the minimum number of colors
assigned to the edges incident to a vertex in $G$. In 2013, H. Li proved that
an edge-colored graph $G$ on $n$ vertices contains a rainbow triangle if
$\delta^c(G)\geq \frac{n+1}{2}$. In this paper, we obtain several estimates on
the number of rainbow triangles through one given vertex in $G$. As
consequences, we prove counting results for rainbow triangles in edge-colored
graphs. One main theorem states that the number of rainbow triangles in $G$ is
at least $\frac{1}{6}\delta^c(G)(2\delta^c(G)-n)n$, which is best possible by
considering the rainbow $k$-partite Tur\'an graph, where its order is divisible
by $k$. This means that there are $\Omega(n^2)$ rainbow triangles in $G$ if
$\delta^c(G)\geq \frac{n+1}{2}$, and $\Omega(n^3)$ rainbow triangles in $G$ if
$\delta^c(G)\geq cn$ when $c>\frac{1}{2}$. Both results are tight in sense of
the order of the magnitude. We also prove a counting version of a previous
theorem on rainbow triangles under a color neighborhood union condition due to
Broersma et al., and an asymptotically tight color degree condition forcing a
colored friendship subgraph $F_k$ (i.e., $k$ rainbow triangles sharing a common
vertex).
