Episode 8: Naru spent all night staring down an evil spirit called an Enmi. When asked why he didn't call Lin, it was because he didn't want to waste his time on something minor and he wanted to see what would happen.
Lin knocking out a possessed guy with approximately no effort at all was pretty dang cool.
Naru destroying a minor god by shooting at it with a cross between his Psychic Powers and the Vajara.
Mai gets her awesome moment during the Forgotten Children arc in the manga. She solved the case almost all by herself, with a little guidance from Gene.
Takigawa unmasking Naru as Oliver Davis. It was a parade of awesome. Some of the others had a part in it, but it was mostly his moment. Naru even declined to comment because he said he didn't want to steal Takigawa's spotlight.
During the Cursed House arc, Naru is rendered unconscious and has to be protected from harmful spirits by a number of charms, including one of Lin's familiars. When one of the possessed family members tries to get at him, the familiar comes to the rescue: out of nowhere, a big green clawed hand lashes out and cuts the guy trying to wake him up. It's awesome, if a little bit frightening.
Takigawa proves his worth here by single-handedly beating back a horde of zombie ghosts and creating a barrier that keeps them away until Lin's familiars returned to take over. He's also the one who dealt the first substantial blow on Okubu-sama.
Ayako finally proving herself as a priestess by purifying dozens of spirits all at once.