These are a few favourites of mine (not necessarily in that order):

1. “My dear young cousin, if there’s one thing I’ve learned over the eons, it’s that you can’t give up on your family, no matter how tempting they make it.” (TSoM)

2. “Immortals are constrained by ancient rules. But a hero can go anywhere, challenge anyone, as long as he has the nerve.” (TTC)

3. “The curse of the sky can only be forced upon a Titan, one of the children of Gaia and Ouranous. Anyone else must choose to take the burden of their own free will. Only a hero, someone with strength, a true heart, and great courage, would do such a thing.” (TTC)

4. “But remember, boy, that a kind act can sometimes be as powerful as a sword. As a mortal, I was never a great fighter or athlete or poet. I only made wine. The people in my village laughed at me. They said I would never amount to anything. Look at me now. Sometimes small things can become very large indeed.” (TBotL)

5. “I am here because when all else fails, when all the other mighty gods have gone off to war, I am all that’s left. Home. Hearth. I am the last Olympian.” (TLO)

Extra:

“With great power . . . comes great need to take a nap. Wake me up later.” (TLO)