Quid rides? Mutato nomine de te fabula narratur - What are you laughing at? Just change the name and the joke's on you. (Horace)
Quidnunc? Or Quid nunc? - What now? As a noun, a quidnunc is a busybody or a gossip
Quidquid agis, prudenter agas et respice finem! - Whatever you do, do cautiously, and look to the end

Quidquid id est, timeo Danaos et dona ferentes

Whatever it is, I fear the Greeks, even bearing gifts. (Vergil)

Quidquid latine dictum sit, altum videtur - Anything said in Latin sounds profound
Quidvis Recte Factum Quamvis Humile Praeclarum - Whatever is rightly done, however humble, is noble
Quieta non movere - Don't move settled things, or Don't rock the boat
Quinon proficit deficit - He who does not advance, go backwards
Quique amavit, cras amet - May he love tomorrow who has never loved before;
Quis custodiet ipsos custodes - Who shall keep watch over the guardians? (Luvenalis) Don't assign a fox to guard the henhouse