Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for Rössler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of Rössler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various Rössler systems with standard parameters is checked numerically.