Episode 13 of Nichijou is my personal favorite. This is the first episode I have seen that doesn't stick to just basic humor, but goes into a very touching story about the relationship between Nano and Professor.
It begins when Sakamoto sees Nano staring at a group of girls happily walking to school and talking about their after-school plans. Sakamoto tells Professor that it looks like Nano wishes she could go to school. This realization scares Nano to tears and she tells Nano not to ever leave her.
The show continues in normal Nichijou fashion, but returns to Professor waking up during a thunderstorm. She fearfully climbs into bed with Nano for protection. She has to use the bathroom, but Nano will not wake up to go with her so she decides to hold it. When Nano does finally awaken, she takes her to the bathroom. Along the way Nano becomes fearful of the thunder as well. Professor then tells her not to be afraid because they are there to protect each other. Nano agrees, and after a short pause, Professor asks her if she wants to go to school. Nano lies and tells her that she doesn't want to go anywhere, but it is apparent that she really does.
The following day Professor comes to Nano telling her excitedly that she will start school tomorrow, and presents her with her uniform.
This episode really tugs on the heart strings and shows that the creators of Nichijou not only can make very great comedy and randomness, but are also very skilled in character development. I hope to see much progression between Nano and Professor in the future.