In this paper, we propose some sparsity aware algorithms, namely the Recursive least-Squares for sparse systems (S-RLS) and l0-norm Recursive least-Squares (l0-RLS), in order to exploit the sparsity of an unknown system. The first algorithm, applies a discard function on the weight vector to disregard the coefficients close to zero during the update process. The second algorithm, employs the sparsity-promoting scheme via some non-convex approximations to the l0-norm. In addition, we consider the respective versions of these algorithms in data-selective versions in order to reduce the update rate. Simulation results show similar performance when comparing the proposed algorithms with standard Recursive Least-Squares (RLS) algorithm while the proposed algorithms require lower computational complexity.