Kyon used to believe in the supernatural, no, not Santa Claus, but things like aliens or ghosts. But reality's crudeness made him realise that they just don't exist, and as he graduated from Middle School he threw all his childish dreams about monsters, superheroes and so on, over board. Now his first High School year has begun, with him thinking that a new more mature life will await him, but during the class introductions he gets to meet a stunning girl, Suzumiya Haruhi, who blatantly claims that she has no interest in common humans, and that she's solely interested in time travelers, sliders, aliens, or espers and would hope that if there are any in the class present that they should join her. At first he thinks that she's just kidding around, but then he realises what stern seriousness was involved in her introduction speech. Surely, his High School years will be anything but normal.
The two are sightly different and have not much in common, but a lot of humorous elements are shared between the two. After watching one of them, you might want to watch the other to change the setting, but still to watch something that deals with supernatural powers and energetic characters learning in school.