Pluripolarity is a quite subtle property.

E. Bedford characterized pluripolar real-analytic submanifolds. For example, all real analytic curves in $\mathbb{C}^n$ are pluripolar for $n>1$.

In opposite direction, it's useful to know examples of sets that are not pluripolar. There is a very surprising example due to K. Diederich and J. E. Fornæss (1982) of a non-pluripolar $C^\infty$ smooth curve in $\mathbb{C}^2$. This construction can be extended to $\mathbb{C}^n$.

Pluripolarity is a quite subtle property.

E. Bedford characterized pluripolar real-analytic submanifolds.

Added: Bedford (in Lelong-Skoda seminar, 1981) called a real submanifold $M$ of $\mathbb{C}^n$ a generating at a point $p$ if the tangent space $T_p M$ is not contained in a proper complex-linear subspace of $\mathbb{C}^n$. It is easy to see that a generating at any point submanifold is not pluripolar. Bedford prove that a real-analytic nowhere generating submanifold is pluripolar.

For example, all real analytic curves in $\mathbb{C}^n$ are pluripolar for $n>1$.

In opposite direction, it's useful to know examples of sets that are not pluripolar. There is a very surprising example due to K. Diederich and J. E. Fornæss (1982) of a non-pluripolar $C^\infty$ smooth curve in $\mathbb{C}^2$. This construction can be extended to $\mathbb{C}^n$.