Molecular dynamics simulations of a simple, bead-spring model of semiflexible polyelectrolytes such as DNA are performed. All charges are explicitly treated. Starting from extended, noncondensed conformations, condensed structures form in the simulations with tetravalent or trivalent counterions. No condensates form or are stable for divalent counterions. The mechanism by which condensates form is described. Briefly, condensation occurs because electrostatic interactions dominate entropy, and the favored coulombic structure is a charge-ordered state. Condensation is a generic phenomenon and occurs for a variety of polyelectrolyte parameters. Toroids and rods are the condensate structures. Toroids form preferentially when the molecular stiffness is sufficiently strong.