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Let $(A,{\mathfrak m})$ be a Cohen-Macaulay local ring and let $I$ be anideal of $A$. We prove that the Rees algebra ${\mathcal R}(I)$ is an almostGorenstein ring in the following cases: (1) $(A,{\mathfrak m})$ is atwo-dimensional excellent Gorenstein normal domain over an algebraically closedfield $K \cong A/{\mathfrak m}$ and $I$ is a $p_g$-ideal; (2) $(A,{\mathfrakm})$ is a two-dimensional almost Gorenstein local ring having minimalmultiplicity and $I={\mathfrak m}^{\ell}$ for all $\ell \ge 1$; (3)$(A,{\mathfrak m})$ is a regular local ring of dimension $d \ge 2$ and$I={\mathfrak m}^{d-1}$. Conversely, if ${\mathcal R}({\mathfrak m}^{\ell})$ isan almost Gorenstein graded ring for some $\ell \ge 2$ and $d \ge 3$, then$\ell=d-1$.

Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals