A cheap way to get a general view of the city is using the METROBUS pass in the EMT urban buses. The most interesting lines are:
* CIRCULAR # C2 (around downtown, counter clockwise):
Glorieta de Embajadores (1) - Ronda de Atocha/Sta. Mª Cabeza (2) - Intercambiador Atocha (3) - Paseo de la Reina Cristina - Doce de Octubre/Narvaez (4) - Narvaez - O'Donnell - Jorge Juan - Doctor Esquerdo - Plaza Manuel Becerra - Francisco Silvela - Fco. Silvela/Av.America (5) - Joaquin Costa - Raimundo Fdez. Villaverde/Pº Castellana (6) - Raimundo Fdez. Villaverde - Cuatro Caminos - Reina Victoria - Juan XXIII - Isaac Peral -Arcipreste de Hita - Princesa - Pza España/Cta.San Vicente (7)(8) - Cta.San Vicente/Principe Pio (9) - Virgen del Puerto - Ronda de Segovia - Ronda de Toledo/Ribera (10) - Glorieta de Embajadores...
Nearby venues:
(1) La Casa Encendida Exhibition Centre
(2) Reina Sofia Modern Art Museum
(3) Puerta de Atocha rail station (AVE trains)
(4) El Retiro park
(5) Intercambiador Avenida de America. Underground bus terminal to airport, Basque Country, Santander, Rioja, Navarra, Burgos, Soria, Guadalajara
(6) Intercambiador Nuevos Ministerios. Metro line to airport.
(7) Bronze sculptures of Don Quixote & Sancho Panza
(8) Egyptian Temple of Debod to honour the gods Amon and Isis
(9) Intercambiador Principe Pio. Underground bus terminal to Segovia.

(10) El Rastro flea market on Sat & Sun

 
* CIRCULAR # C1 (around downtown, clockwise)
* Line # 27 (South - North):
Glorieta de Embajadores (1) - Ronda de Atocha - Paseo de las Delicias/Tortosa (2) - Paseo Prado/Pza Murillo (3)(4)(5) - Paseo del Prado - Pza.Canovas del Castillo (6) - Paseo del Prado/Pza.Cibeles (7) - Paseo de Recoletos/Biblioteca Nacional (8)(9) - Paseo de la Castellana - Pº Castellana/Gta.Emilio Castelar (10) - Pza. San Juan de la Cruz (11) - Pª Castellana/Pº La Habana (12) - Pº Castellana/Pza. Lima (13) - Plaza Cuzco - Plaza Castilla (14)
Nearby venues:
(1) La Casa Encendida Exhibition Centre
(2) Reina Sofia Modern Art Museum
(3) Caixa Forum Exhibition Centre
(4) Botanical Garden
(5) Museo del Prado
(6) Museo Thyssen-Bornemisza
(7) Ayuntamiento (Town Hall)
(8) Biblioteca Nacional (National Library)
(9) Museo Arqueologico Nacional
(10) Museo Sorolla
(11) Museo de Ciencias Naturales
(12) Intercambiador Nuevos Ministerios. Metro line to airport
(13) Estadio Santiago Bernabeu (Real Madrid soccer stadium)

(14) Torres KIO buildings with an inclination of 15 degrees.

 
* Line # 2 (West - East):
Guzman el Bueno - Princesa - Gran Via/Pza.España (1)(2) - Gran Via - Callao - Gran Via/Alcala (3)(4) - Plaza Cibeles (5) - Puerta de Alcala (6)(7)- Alcala - O'Donnell - Doctor Esquerdo - Plaza Manuel Becerra
Nearby venues:
(1) Bronze sculptures of Don Quixote & Sancho Panza
(2) Egyptian Temple of Debod to honour the gods Amon and Isis
(3) Metropolis building
(4) Circulo de Bellas Artes
(5) Ayuntamiento (Town Hall)
(6) Puerta de Alcala. City gate built in the 18th century.
(7) El Retiro park
 
The 10 rides pass called METROBUS (€ 6.70) is valid on both systems: EMT urban buses and Metro, but it is NOT VALID for buses to the extended metropolitan area (green buses). You can share your METROBUS pass with other people.
How to buy a METROBUS pass? Using the automatic ticket machines in any Metro station. It's also on sale for the same price in 'estancos' (tobacco shops). Advise: the METROBUS pass IS NOT ON SALE on board the EMT urban buses.
Other possibilities:
* Sight-seeing hop-in hop-off buses:
http://www.madridvision.es/en/index.php
* Organized tours:
http://www.esmadrid.com/monograficos/...
http://www.wellsoc.org/WellingtonTour...
http://www.madsegs.com/