Pashupatinath Temple

This is a UNESCO World Heritage Site, but only Hindus are allowed entrance. Pashupati is complex of buildings on the bank of the Bagmati river. You can find temples, ashrams, and artistic carvings in the primary temple complex. Outside the temple funeral pyres are routinely held and the ashes are freed in the river.
A small zoo is located above Pashupatinath in a park. It is fitting, because the deity Pashupati is considered lord of animals. Pashupati is important in Hinduism, because it is identified as one of the homes of Shiva as out-lined in the ancient text Paadal Petra Sthalams.
To see other important UNESCO World Heritage Sites you can follow these links: Boudhanath Stupa, Patan Durbar Square, Swayambhunath, or see them all.

History
Pashupati was originally built in the 3rd century, but has been rebuilt several times since. The current version of the temple was built by King Shupuspa in the 15th century. In addition, the Guhyeshwari Temple was built in the 11th century, and the Ram temple was added in the 14th century.
Mythology

There are several myths surrounding Pashupati. My favorite myth is:
One day Lord Shiva was walking around on earth and he came to Bagmati River, which he believed to be one of the most beautiful sites in the world. He fell in love with the area, and turned himself into a deer. He spent many years in this form. Because he grew missed by his deity friends, they came and grabbed him forcing him back into his original form.
Lord Shiva announced, after he returned to his divine form, that he will be known as the Lord of Animals.
How to find Pashupati
Pashupatinath Temple is located 2.5 miles east of Thamel. It is a 15 minute drive, but if there is traffic, it can take up to 40 minutes. You can walk there without too much trouble, because it is a short distance.
When to go

You can visit Pashupati anytime because the area is always open. You can see the funerals and zoo during the day and the lighted temple at night. If you are Hindu, you can enter the temple between 4am and 9pm.
How long to stay
Because you will probably not be able to enter the temple, you will want to spend at least 1 hour in Pashupati. If you are Hindu, you will want to visit for at least 2 hours.