The Lattice Boltzmann approach for fluid dynamics is used to compute the drag force on various types of obstacles in two-dimensional flows. We study the finite size effects for the drag force on a cylinder and propose a scaling law. Then we consider the hydrodynamic behavior of fractal objects and compare the drag force they experience with that of simpler geometries. Simulation results show that, in 2D, the outer shape of the fractal plays the main role to determine the drag whereas the internal structure has little influence. Finally, the effect of fractal compacity on the hydrodynamic properties is also discussed. Since the fractal dimension and the outer radius of the aggregate are related, a dependence of the hydrodynamic properties on the fractal dimension can be established.