There are countless amazing ones but just curious if there are any that are burrowed in deep and won't leave. For me there are two.
"The first duty of every Starfleet officer is to the truth, whether scientific truth, historical truth or personal truth. It is the guiding principle on which Starfleet is based so if you can't find it within yourself to stand up for the truth then you don't deserve to wear that uniform." -Picard
"‘Why me?’ It’s the question you ask yourself every morning and every evening. No one else gets a second chance so why me? That led you to the idea that there was a reason for your survival, a purpose you’re meant to fulfill, right here, right now. And that led you to a savior complex because if there is no reason, if there is no purpose, then your very existence is a middle finger to anyone who has ever lost someone. Which is everyone. How’s that for brutal honesty?" -Kovich
This, but not even in a joking way; In The Pale Moonlight was my late best friend's favourite episode of Trek, and I watched DS9 with him. This line will always make me think of him