Loads and loads of options in Cuzco to suit all budgets. Most won't need to be booked beforehand.

Budget
Hospedaje El Artesano de San Blas, Suytucato 790 (straight up from the Plaza San Blas), ? +51 84 263-968. Well-kept place with good-value rooms around a colonial courtyard, hot water, common kitchen, helpful staff, wifi 20-40 soles. 
Taita Home, Suytucato 759 (straight up from the Plaza San Blas, there is no sign on the door). Dormitory beds in a freaky, chilled out and friendly atmosphere with a sunny garden, fireplace, outdoor kitchen and gas hot water. 15 soles. 
Semanapata, Siete Angelinos (Las Blas). checkin: from. Hostel in San Blas area of Cuzco, about 3 blocks from Plaza de Armas. Free wifi, 2 free computers, free breakfast, all rooms have cableTV. Very friendly staff, rooms cleaned daily. Much cheaper than similar places. Opened in May 2011. from 25 Soles per person. 
San Blas, many new hospedajes/hostales have opened in this area 4 blocks up the hill from the Plaza de Armas.
La Casa de la Abuela, Urbanizacion Zaguan Del Cielo 0-17B (Lucrepata costado del Mercado San Blas), ? +51 84 301666, +51 84 733964. checkout: 12 noon. Cheap place to sleep with lean rooms, high speed internet/wifi, 10 min walk to Plaza de Armas. Bathrooms are not very clean-bring sandals. No access by taxi, foot access only. Some may find the beds a little hard. 2 soles double, 25 soles triple/room. 
La Casa de mi Abuelo, Nueva Alta 785. A new guesthouse near the Plaza de San Francisco run by a kind local lady that offers extremely clean and comfortable rooms, ensuite bathrooms, cableTV, and excellent breakfasts. 7 minute walk to Plaza de Armas US$20 double, US$13 single,. 
Pirwa Hostel Colonial Cuzco (Pirwa backpackers hostel), San Francisco #360 (San Francisco square), ? +51 84 244315. 24 hr hot showers, movies, in-house bar, pool (game) table, attentive staff, free breakfast, free internet, pick up service, and comfortable beds. From US$7.50/person. 
Pirwa Bed&Breakfast Posada del Corregidor Cusco (Pirwa b&b hostel Cusco), Portal De Panes #151 (Main square of Cusco), ? +51 84 244315. Movies, safe and relaxed environment, traditional meals, good view of the main plaza. From US$10.00/person. 
Pirwa Bed&Breakfast Suecia Cusco (Pirwa b&b hostel Cusco), Suecia #300 (Just off the main square of Cusco), ? +51 84 244315. Close enough to everything you might need yet quiet. TV in room, roofed patio. From US$25.00/person. 
Pirwa Backpackers Familiar Cusco (Pirwa backpackers hostel Cusco), Carmen Alto #283 (San Blas - Cusco), ? +51 84 244315. In the artistic quarter of town. Fairly small, but still big enough to meet new people. Comfy sofas to read a book or watch a movie. From US$7.50/person. 
Yamanyá Backpackers, San Andres 260, ? +51 84 224473 . In a beautiful and funkily decorated colonial home with two patios and a back garden (complete with giant heated jacuzzi for 20 people), good beds with feather duvets. Hot showers, free wifi and internet, cable TV, DVDs, big screen high-def LCD, free breakfast, big guest kitchen, bar with great activities and weekly pub crawl. Good staff and helpful tour agency. Two blocks from the Plaza de Armas.
Casa de la Gringa, ? +51 842 41168. Each room has a different theme and features original interntaional art. Comfortable and colorful. Free wifi, cable TV and DVDs, common rooms, a beautiful garden, and good staff.
Hogar Clinica San Juan de Dios, Avenida Manzanares 264 (Urbanizacion Manuel Prado), ? +51 842 40135. Private and double rooms and windows that look onto the mountain range. Good service and daily egg breakfast. Non-profit hostel supporting the children's hospital next door.
Pariwana Hostel, Meson de la Estrella 136. Two blocks from the Plaza, hot showers, common areas are decorated with local designs, safe, clean.
Casa de la Gringa 2, Carmen Bajo 226, ?+51 842 54387. Small friendly hostel is the little sister to Casa de la Gringa, and run by the same helpful owners. Long-term prices available. Can organize tours and special trips to the mountains. Rooms a bit small, wifi, no TVs. 40 soles includes breakfast.
Flying Dog Hostel Choquechaca 469. ?+51 842 53997 Great hostel with a wide range of rooms. Free wifi (in lobby, not room), breakfast, lockers, and coffee and tea all day. Check out their bar, and ask them to arrange tours for you. Friendly staff.
Hospedaje Estrellita, Avenida Tullumayo 445. Shared double rooms surround a large concrete courtyard. There is a kitchen with a sociable commonroom with cableTV. A night cost 15 soles and includes a small breakfast. It's popular with gringos.
Loki Backpackers Hostel Cuesta Santa Ana #601, Centro Historico, ?+51 842 43705. 180 beds, noisy party hostel in a 450 year old Peruvian national monument. Dorms from US$6, basic breakfast included. Wifi, tea and coffee are included. Hot water with pressure in generally shared showers. 1PM checkout and small lockers in reception that have plug sockets in them.
The WalkOn Inn, Calle Suecia 504, ?+51 842 35065, has very beautiful rooms with private or shared bathroom and two small dorms. The place has a nice patio with a fireplace, it's completely clean and there is another sitting room with tv and cable and a computer with free internet on which to burn your own CDs or DVDs. Free wifi, laundry service, breakfast available. 2 blocks from the main square, close to the centre of 'fiesta'. Pressurized hot water available around the clock.
Casa Arco Iris, Calle Arco Iris 535, Barrio San Cristobal, ?+51 842 47526. In a centuries old building, friendly owners. Opened in early 2006, calm and quiet. Rooms from US$4.
Rimacpampa Hostal, Close to the plaza. Amazingly hot showers, with good water pressure. TV, food available.
Home Sweet Home-El Mirador, Asociacion San marcos A-3.San Blas. ?+51 842 231235. Nearby to small bars, restaurants and cafes. Free internet and wifi throughout, hot showers, towels available, and warm bed available. Use of kitchen. Only 6 blocks from the main square.
Hostel Sweet Daybreak, Calle Pasñapakana 133, Mirador de San Blas, ?+51 842 225776. Panoramic views, showers with hot gas-heated water 24 hr, cableTV, wifi, laundry, cafeteria, free tourist information, a lovely garden, dormitories, private rooms with or without bathroom. Comfortable and safe, a 2 minutes walk from the Plazoleta San Blas, 4 blocks from the Plaza de Armas (Main Square).
Hospedaje Corona Real, Ave Huascar 226. Quiet and cheap option about 15 min walk from the city center. Rooms are spacious and have private bathroom and local television and cost 15 soles per person.
Hostal Familiar, Calle Saphi 661, (3 blocks from Plaza de Armas). Singles US$8 with private bathroom and hot water.
San Blas Hospedaje, In the heart of San Blas. Nice interior sitting area, some rooms have views. CableTV, wifi. Rooms basic but clean and nice. Family-run. Hot water 24 hr. 60 soles includes breakfast.
Hostal Central Choquechaca #298. A new, affordable, simple but clean hotel in the heart of San Blas. Some rooms have views onto the street, others are to interior courtyard. No breakfast, no internet. 30 soles.
Qori Ñusta Inn Calle Chiwampata 515, (on the edge of San Blas), ?+51 842 228299. Breakfast, cableTV, wifi, friendly staff. Large rooms some with desks and refrigerator. Posted prices are high, but they can be talked down to 45 soles per night.

Mid-range
Piccola Locanda, [Resbalosa 520. Very quiet, beautiful rooms, clean and cozy, 2 block from plaza de Armas. The Locanda contributes to the financing of 3 projects dedicated to children and has an internet cafè and a travel agency. Quiet, rooms are decent sized and have private or shared bath facilities and TV. US$30-55/room depending on type of bed(s), occupancy and season.
Amaru Hostal I, Cuesta San Blas 541, Quiet and cheap option about 3 blocks from the Plaza de Armas. Rooms are decent sized and have private or shared bath facilities and TV. US$30-55/room depending on type of bed(s), occupancy and season.
Amaru Hostal II, Chihuampata 642. Quiet and cheap option about 2-3 blocks from the Plaza de Armas. US$30-48/room depending on type of bed(s), occupancy and season.
Hotel El Balcon, 222 Tambo de Montero, a short distance from Plaza de Armas, awesome interior design, delicious breakfast and moderate prices. From Plaza de Armas, follow Plateros a block and a half or so. The hotel is in a lane up the hill. About half a block up, look for the door on the right. The sign is above the door, so you may not see it unless you walk on the opposite side of the lane.
Hostal Frankenstein, San Juan de Dios 260, (2 blocks from main square). Clean, friendly and helpful German chef, a lazy iguana, creative interior, cosy atmosphere. Double costs around US$20 (the one on top is quiet and offer view to Ausangate mountain).
Hoteles Garcilaso, Calle Garcilaso 233-285. ?+51 842 233031, +51 842 233501, +51 842 227951,+51 842 222425. There are two of them on the same block. Good location on the block between the Plaza San Francisco and the other small plaza that is one block from the Plaza de Armas. As in a lot of places, the inside rooms may be the way to go because they are quiet at night. Double US$75 dollar/night, however It is worth more like US$30-45/night.
Orquidea Real, Calle Alabado 520, The colonial building has original Inca walls and exposed wood beams, and the rustic accommodations are simply decorated in a cozy mountain lodge aesthetic. All rooms are oriented toward Cuzco below, offering panoramic views.
Madison Hostel, Av Pardo 721. ?+51 842 25995. Friendly, family-run hotel located on a quiet, safe street four blocks from the Plaza. Rooms include cable TV, big buffet breakfast, wifi, and views. Children under 12 stay for free.
Gran Hostal Machu Picchu, Calle Quera 282, ?+51 842 84 23 1111.
Hostal Rumi Punku, Calle Choquechaca 339. Rumi Punku means "stone door" in Quechua: the entrance to the hotel leads through an ancient stone door, obviously of Inca design. The doorway is all that has survived of an Inca palace. The door is considered a historic item by the city of Cusco.
Casa San Blas Boutique Inn, Tucoyeros 566, San Blas. In the historic artisan's quarter 2.5 blocks from the main square in a neighborhood of narrow, cobbled streets and whitewashed colonial-era houses. Friendly staff. US$110 a night for a single.
Koyllur Hostal, Calle Carment Bajo 186, San Blas. . Richly decorated and a nice place to splash out for a few nights. Big buffet breakfasts. Ask for room at top floor in the front - has skylights, lots of room, nice furnishings. CableTV, wifi. US$20 in off-season.

Splurge
Libertador Palacio del Inka, 4 Bustos house, In the center of the city. The hotel was part of the Koricancha temple and during colonial times it became property of the conqueror Francisco Pizarro.
Amerinka Boutique Hotel. Modern hotel that combines warm room atmospheres with professional and experienced attention. Well located near Plaza de armas
The Garden House Hotel, ?+51 842 271117. Family-run boutique hotel in a private garden. Modern decor, wifi.
Hotel Royal Inka I or II, (in front of the Plaza Regocijo, about 150 m from la Plaza de Armas). Royal Inka I is a renovated house while Royal Inka II is more modern with a spa (jacuzzi and steam room). Breakfast available.
Hotel Monasterio, Calle Palacios 136, Plazoleta Nazarenas, ?+51 842 41777, Housed in a former monastery, rooms are former monks' cells, but they are far from monastic. By far the most expensive place to stay Cuzco. Avoid rooms 414-419, which are near a noisy generator.
Hotel Marqueses, Calle Garcilaso N° 256, ?+51 842 264249. The official hotel of SAS travel. Good staff and comfortable rooms. Centrally located in the tourist district, only 2 blocks from the Plaza des Armas.

Related Links:
Lima Peru Guide
Cusco Hotel Reservation