Not precisely homophones, I still hear these words used in each other's place in conversation and see them switched from time to time in such literary masterpieces as blog posts, status updates, and user comments. I can understand why – they're tricky to spell, similar in meaning, and also similar in pronunciation. But they're not interchangeable.
Conscience [kon-shence] – (n.) your personal set of morals.
Conscious [kon-shuss] – (adj.) awake, aware, not asleep.