Fushimi Inari Taisha
Predating the capital of Heian-kyô in the 8th century, Fushimi Inari Taisha is one if not the most iconic shrine known to foreigners around the world. Home of Ukanomitama-no-Mikoto, the goddess of agriculture, the shrine is dedicated to the well being of crops. The shrine has had many famous donors over the years, including famed warrior Toyotomi Hideyoshi who donated the front gate of the shrine. Unlike most other shrines, Fushimi Inari ranges all over a single mountain from the main shrine at the bottom to the "center" of the shrine at the top where a flame is lit.
For the casual: 10. For the educated: 10
The shrine's inconicity is derived from two key features: it's tori gates and its fox statues. Foxes are the messengers of the goddess and are known for hunting many of the pests that would harm agricultural fields. Now if you've read my Intro to Shrines page, which I highly encourage you do if you haven't yet, you'll know that all shrines will have a tori gate. This gate signifies the boundary between the worlds of mortals and immortals, the sacred and impious. Fushimi Inari on the other hand doesn't have one, two, or ten, it has thousands upon thousands of tori gates which align the twisting pathways that lead from the base of the mountain, to smaller shrines across the mountain, and finally to the "center" of the main shrine at the summit of the mountain. These tori gates are all donations from various individuals and companies over the years and by stacking them closely together, the viewer gets the illusion of walking through vermilion hallways. In fact, at the entrance to the main shrine, there are even notices letting visitors know how much one tori will cost ranging from small tori only about a food tall, to one of the many thousands of large tori which mark the main pathways up the mountain.
Because Fushimi Inari Taisha is a celebrety amongst shrines across Japan, be prepared to face large crowds if visiting on a weekend or on a holiday. An easy way to avoid most crowds on any day is to visit around noon (all the tours arrive in the morning) or on a weekday. If you're not interested in climbing the mountain, that's totally fine, but the majority of visitors will be staying close to the base of the shrine and some of the first few hallways of vermillian tori before leaving for the next major tourist attraction. All the same, I don't believe that a visit to Kyoto is complete without visiting Fushimi Inari Taisha.