My favorite ground cover which tolerates shade is sweet woodruff. Tolerant of shade and drought, after established, spreads nicely, very pretty white flowers, and easy to pull up if it goes where you don't want it.
Lily of the valley is pretty quick spreading and shade tolerant; it is well behaved if not over-watered, but can wander into nearby grass. But what wonderful flowers!
Myrtle, of course, is well known and spreads quickly; blue flowers, and easy to find in the stores.
Lamium maculatum (has the unpleasant name of "dead nettle") is a quickly spreading ground cover; it has very attractive green leaves that look like they were painted with gray; very attractive yellow flowers (like snapdragons, sort of) this time of year (late May); can be quite aggressive, however, so make sure you plant it where you want it and where you don't mind it roaming.
Ivy spreads fast, but will climb trees (damage-causing is a great source of debate); again, make sure you want it where you plant it. But, relatively easy to pull up the runners, if you catch them soon enough.
Another idea is some of the geraniums (not the pelagoniums you see in the pots). I planted geranium 'Claridge Druce' years ago and it has become a groundcover from which I dig "babies" every year.
Hope this gives you a start!