Speed has no effect in battles, but on the main map your ships' speeds are 1 + any engines + your civ's speed bonuses.

You can spend ability points for speed bonuses during game setup, and the propulsion tech tree has a few 'milestone' techs that give all your ships +1 speed even if they have no engines. Some techs also give a speed bonus directly, such at the Thalan's Expert Gravity Channeling, or indirectly, such as when Zero G Sports Arenas enable you to build the Gravity Accelerators trade good.