In this paper we study the classification polynomial vector fields with isolated singularities on ${\co}^2$ under the hypothesis that the non--singular orbits are simply--connected. Also we regard the case these orbits are {\em cylinders}. Regardless the natural relations with the study of complete vector fields on $\co^2$ which is carried out in \cite{Ce-Sc}, we give examples where the vector field is not complete. Our techniques are based on the geometry of the corresponding projective foliation.