Quem di diligunt, adolescens moritur - Whom the gods love die young. (only the good die young)
Quemadmodum possums scire utrum vere simus an solum sentiamus nos esse? - How are we to know whether we actually exist or only think we exist?
Quemadmoeum gladis nemeinum occidit, occidentis telum est - A sword is never a killer, it's a tool in the killer's hands. (Seneca)

Qui bene cantat, bis orat

He who sings well, prays twice

Qui bono? - Who benfits?
Qui dedit benificium taceat; narret qui accepit - Let him who has done a good deed be silent; let him who has received it tell it. (Seneca)
Qui desiderat pacem, praeparet bellum - Let him who wishes for peace prepare for war. (Vegetius)
Qui docet discit - He who teaches learns
Qui dormit, non peccat - One who sleeps doesn't sin
Qui habet aures audiendi audiat - He who has ears, let him understand how to listen