For five nights around the full moon the Taj by Moonlight is open to groups of 50 people in a series of eight 30-minute time slots between 8.30pm and 12.30am. You can only view the Taj from the entry gate viewing area and you only get 30 minutes there, making this an expensive option, but some people love it. The later time slots are best for moonlight views.
Tickets must be bought a day in advance from the Archaeological Survey of India office; see its website for details. (Note: this office is known as the Taj Mahal Office by some rickshaw riders.) You need to go through security clearance at the Shilpgram Tourist Facilitation Centre first, before being taken by security on an electric bus to the eastern gate.