  We prove that on $X_n$, the plane blown--up at $n$ general points, there are
Ulrich line bundles with respect to a line bundle corresponding to curves of
degree $m$ passing simply through the $n$ blown--up points, with $m\leq
2\sqrt{n}$ and such that the line bundle in question is very ample on $X_n$. We
prove that the number of these Ulrich line bundles tends to infinity with $n$.
  We also prove the existence of slope--stable rank--$r$ Ulrich vector bundles
on $X_n$, for $n\geq 2$ and any $r \geq 1$ and we compute the dimensions of
their moduli spaces. These computations imply that $X_n$ is {Ulrich wild}.
