We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free energy landscape. Melting profiles, dependence of melting temperature on loop length, and kinetic time scales are in semiquantitative agreement with experimental data obtained from fluorescent DNA beacons forming poly(T) loops. Variation in strand rigidity is not sufficient to account for the large activation enthalpy of closing and the strong loop length dependence observed in hairpins forming poly(A) loops. Implications for modeling single strands of DNA or RNA are discussed.