Varanasi is not a city with distinct tourist destinations as such: instead, the experience is in watching the spectacle of life and death on the river and meandering through the alleys of the old city.
also known as the Golden Temple, security is tight making entrance difficult and sometimes completely off limits to foreigners. No bags, cellphones or pens are allowed. They can be deposited in the shops by the temple entrance.
Nepali Hindu Temple
A small golden temple, built in Nepali architecture, near Lalita Ghat
overlooking Panchganga Ghat, it's a great place for a bird's eye view of the area.
Man Mandir Observatory
Tulsi Manas Temple
Banaras Hindu University
a very green and peaceful campus. There is also a Vishwanath Temple bulit by Pt. Madan Mohan Malviya.
Ram Nagar Fort
the fort of the King of Kashi
A ghat is a series of steps leading down to the river, used by bathers and pilgrims, and riverside Varanasi consists of a long sequence of these. It's generally possible to walk directly between them, though near Manikarnika Ghat you'll have to navigate your way up and around through the alleyways. The best option for viewing the ghats is to charter a boat and see them from the river.
Hindus consider it auspicious to die in Varanasi, so some ghats are known as burning ghats, where bodies are cremated (in full view) before their ashes are placed in the Ganges.
the ghat on which bathing with spouse is not advised because the myth of contention
the meeting of the five rivers
the main cremation ghat; a must-see, but remain quiet and never take photographs
the main ghat and site of the large evening aarti; only reachable by foot at some times of day, about a 5 minute walk south from Godaulia
brightly painted in stripes and busy with bathers, very photogenic
the cremation place were Raja Harishchandra did the last rituals of his son.
site of the large water purification plant
a popular place to stay with many hotels, restaurants and internet cafes
Varanasi is a good place to learn a classical instrument such as the tabla or sitar - many teachers can be found throughout the city, but quality varies considerably so ask around and check out a few.
Yoga is also popular, and the same rules apply.
Benares Hindu University  offers a wide range of classes on topics related to classical Indian studies in English.
Diwali is a great time to be in Varanasi, with special preparations going on in many temples. The once-in-a-year decorations and aarti at the ghats are spectacular.
Shivaratri is another great time to be in varanasi. The day of Shivaratri is also the last day of the Dhrupad Mela, a festival of classic indian music going on night and day for three days.
Varanasi is famous for its fine silk - it's on offer everywhere, but shop around and bargain hard!
Mehrotra Silk Factory, (near Brahma Ghat, follow the multiple yellow signs) has set, reasonable prices and a good selection. A little out of the way, but worth the trip.
Wow India, Assi Ghat (the big corner shop, follow the tourists). A large collection of handicrafts from all over the country, a good place to pick up your gifts and souvenirs. Music, silks, ayurvedic cosmetics, herbal teas, incense and plenty more. Prices are moderate and fixed. edit
There are numerous food outlets and a very dynamic range in quality. The restaurants closer to the ghats cater more to foreign tourists, with variable success. To get really authentic Banarasi Khana you're going to have to get to the main market area or, better, to have a banarasi friend inviting you at home. Benares Dum Aloo is a local specialty, and the city is also known for its desserts.
You can't go away from Benares without eating local specialities as aloo chat and pani puri and, in general, the street food. Paan is not really food, but is something Benares is famous for all over India.
Boat rides are very popular, especially at sunrise and sunset. The most popular sunset ride is to start at Dasaswamedh Ghat and head up to Manikarnika Ghat to see the cremations in progress, and then return to Dasaswamedh and watch the evening aarti from the boat. Sunrise is another magical time for a ride, when the ghats are filled with Hindus bathing and starting their day - one of the most famous sights in India.
You can bargain the price down to around Rs 30/person per hour (even for just 1 person in the boat), but expect to be quoted much higher — the current 'tourist' rate for a boat ride is Rs 300! During the trip "market boats" will float up to you selling overpriced trinkets which can be bought much cheaper on land. Any offers of flowers for puja will definitely not be free; Rs 2 per flower bowl and Rs 5 per candle bowl are the going rates, though as a tourist you might be asked for as much as Rs 100 each.
*Get lost in the alleyways - the sounds, sight and smells are just unbelievable!