Two of my favourite games are Ribbon Drive and The Skeletons, and neither use dice (the latter can use dice, but it's not necessary and it's just to randomise something from a table, instead of picking yourself). Dread is also pretty cool and doesn't use dice (a jenga tower instead), and my own game The 5 whys doesn't use them, either (it uses custom cards).
And although strictly speaking it uses dice, I'd say that Fiasco could almost be considered a diceless game.