"The only end of writing is to enable the readers better to enjoy life, or better to endure it."
I like this statement from Johnson--it's so concise, punchy even. It's such a nice answer to the question of why people should ever bother with a task as uncertain as writing.
On this topic, I'm also partial to a line from Sylvia Plath. The poet narrator of Plath's The Bell Jar defends her avocation (in her mind, in response to a condescending remark from her med-student boyfriend) as "writing poems people would remember and repeat to themselves when they were unhappy or sick and couldn't sleep." It struck me the first time I read it, and has remained, one of my favorite explanations for what writers give the world.
Opening doors. Providing illumination, or comfort, or knowledge, or recognition. It's a good enough way to spend a life.
*from Johnson's review of Soame Jenyns' "Free Enquiry into the Nature of the Origin of Good and Evil," per Apocrypha, the Samuel Johnson Sound Bite page