Shrines and Temples

The two main Japanese religions are Shinto (an animistic religion similar to (neo-)Paganism in the West) and Buddhism. A lot of anime action takes place in Shinto shrines and Buddhist temples. Series with a supernatural bent may be set there for part or all of their action. More light-hearted Slice of Life series may feature the characters attending a festival such as Hatsumode (New Year's), possibly as part of a Festival Episode. Famous shrines and temples are also good destinations for a Class Trip.

You may or may not meet a Miko at shrines. Shrines usually will also have shimenawa present.

Anime

 * Ah! My Goddess
 * Asagiri no Miko
 * Azumanga Daioh
 * Blue Seed
 * Dennou Coil features a lot of them; the town the story is set in has a lot of old shrines, and the protagonists are often forced to seek refuge from trigger-happy antivirus program Satchii (who is forbidden from entering shrines and private homes) in them.
 * Fushigi Yuugi (but the temples are Chinese Taoist)
 * In Ghost in the Shell:Stand Alone Complex the prime minister visists a buddhist temple to meditate before a highly critical meeting, where she is attacked by a terrorist with a katana.
 * Haunted Junction (Mutsuki is the daughter of a Shinto priestess, Kazumi is the grandson of a Buddhist priest. Haruto, the only one left out, is the son of a kirishitan (Christian) minister)
 * The rather twisted shrine of Oyashiro-sama in Higurashi no Naku Koro ni.
 * Inuyasha often deals with temples, monks and priestesses. A main character actually lives in a shrine.
 * Kannagi, Nagi is a deity after all.
 * Kannazuki no Miko
 * Kamichu! (Where else would a god hang out?)
 * Kure-nai, the two main protoganists visit a festival at a shrine.
 * Lucky Star (Sometimes a setting in the story as Kagami and Tsukasa's father is a Shinto priest.)
 * The second Monster of the Week battle in Magical Girl Lyrical Nanoha takes place at the entrance of one.
 * The Class Trip Arc of Mahou Sensei Negima includes a visit to a famous temple complex in Kyoto, and Konoka's childhood home is yet another temple complex. There's also the Tatsumiya Shrine, which was used by Chao as the setting for the Tournament Arc of the Mahora Festival.
 * Mai-HiME
 * Marmalade Boy (everyone attends Hatsumode, and Miki visits a shrine in Hiroshima when Meiko runs off to be with Na-chan)
 * The manga of Mermaid Melody Pichi Pichi Pitch. Rina is a miko at a shrine to a mermaid, making one wonder about the head priest...
 * Worth noting: Neon Genesis Evangelion is notable for containing almost no references to Japan's native religion or the most popular imported one, with only two exceptions -- a 108 reference that is quickly passed over, and a hilltop Shinto shrine that is almost demolished in an early episode.
 * Nyan Koi!, it's where all the fun with the cats started.
 * In the Ouran High School Host Club manga the boys, Haruhi, and their new friend Mei all visit a temple for New Year's.
 * Sailor Moon (Rei/Sailor Mars is a Miko at a Shinto shrine owned by her grandfather, and everyone goes to Hatsumode)
 * Tenchi Muyo! (Yosho is the head priest of his own temple and trains Tenchi there. Also, in Shin Tenchi Muyo Tenchi trains under another Shinto priest)
 * In Yotsuba&!, we get both. For the shrines, Jumbo takes Yotsuba and Ena cicada-catching at a local shrine, because of all the trees on the grounds make it a good hunting ground, and the girls later help pull a omikoshi (portable shrine) through the streets during a festival there. For the temples, Yotsuba's father uses a temple guardian statue to scare her after catching her lying one too many times.
 * Shrines show up frequently in XxxHolic, and let's not get started on the shop where Yuuki lives...
 * Touko form Touko no Jikenbo is a young priestess that struggles to keep the family shrine solvent.
 * The girls from Tamayura like to hang out at some well-known temples in their hometown of Takehara, most notably Saihō-ji.
 * Series taking place in the historic town of Kamakura naturally feature a lot of these:
 * Aoi Hana
 * Elfen Lied
 * Twin Spica, mostly through flashbacks.
 * Uta Kata

Video Games

 * Being a Miko, Maori's stage in Arcana Heart is naturally the Shrine her family takes care of.
 * The Hakurei and, later, Moriya shrines in Touhou. The Hakurei shrine is of particular importance: not only is it the home of one of the protagonists, but it also acts as a doorway into and out of Gensokyo. Reimu's so lazy about maintaining it that it's basically lost all of its holiness, though.
 * And as of Undefined Fantastic Object, we can add Byakuren's Buddhist temple to the mix.
 * The local shrine is an important location in Persona 3. You can boost your relationships and Knowledge there, it's where the New Year's Festival is held, and two Social Links hang out at its attached playground(?). It's also where Kuromaru, one of your party members, used to live. (He was the Evil-Detecting Dog.)
 * Persona 4 features a run-down shrine that seems to be abandoned except for a surprisingly money-hungry fox who has you fulfill the prayers of people who visit in exchange for discounts on healing in the TV World.

Western Animation

 * Avatar: The Last Airbender makes rather generous use of this trope - much of the action in the Season 1 finale takes place in an oasis at the North Pole, which can only be called a 'shrine' to the Ocean and Moon spirits . In episode three, when Aang first tastes the Avatar State, shrines and temples to the Avatar all over the world are shown lighting up in sympathy with him. We later see a temple dedicated to the Avatar in the Fire Nation, and a shrine devoted to Avatar Kyoshi in her home island. There's also the four Air Temples.