If I'm writing and emotional piece, I want them to feel a connection. If I'm writing a useful piece, I hope they feel a sense of gratitude and gain. If I'm writing a factual piece, I hope they feel more knowledgable.
Regardless of what I write, I hope they don't ever feel like it was a waste of their time. I try to put myself in the place of the reader and think "If the piece wasn't my "bag", would I still feel it was well written and a complete thought?"