Context. Observational and theoretical studies suggest that there are many and various planetary systems in the Universe. Aims. We study the formation and water delivery of planets in the habitable zone (HZ) around solar-type stars. In particular, we study different dynamical environments that are defined by the most massive body in the system. Methods. First of all, a semi-analytical model was used to define the mass of the protoplanetary disks that produce each of the five dynamical scenarios of our research. Then, we made use of the same semi-analytical model to describe the evolution of embryos and planetesimals during the gaseous phase. Finally, we carried out N-body simulations of planetary accretion in order to analyze the formation and water delivery of planets in the HZ in the different dynamical environments. Results. Water worlds are efficiently formed in the HZ in different dynamical scenarios. In systems with a giant planet analog to Jupiter or Saturn around the snow line, super-Earths tend to migrate into the HZ from outside the snow line as a result of interactions with other embryos and accrete water only during the gaseous phase. In systems without giant planets, Earths and super-Earths with high water by mass contents can either be formed in situ in the HZ or migrate into it from outer regions, and water can be accreted during the gaseous phase and in collisions with water-rich embryos and planetesimals. Conclusions. The formation of planets in the HZ with very high water by mass contents seems to be a common process around Sun-like stars. Our research suggests that such planets are still very efficiently produced in different dynamical environments. Moreover, our study indicates that the formation of planets in the HZ with masses and water contents similar to those of Earth seems to be a rare process around solar-type stars in the systems under consideration.