Of approximately 300 km of metro lines in Spain's capital, more than 100 km have been built in just a few years around the turn of the millennium. Many of the newer stations and some of the older ones have interesting designs or architecture.
Photo [wikimedia.org]: Entrance building of Lago station of 1961.
Photo [unknown origin, skyscrapercity.com]: Nuevos Ministerios station in Madrid, inaugurated in 2002.
Tours of the metro system, guided by experts. For dates and reservation contact the tour operator or check their website.
A guide accompanies you to normally inaccessable places. Includes the Anden 0 Chamberi exhibition and museum metro station as well as archaeological displays in another station. Fee: 30 euros. Tour operator: getyourguide.com.
Try the following tour, recommended by residents or metro enthusiasts:
Interesting stations on line L8 are Campo de las Naciones (one station away from Aeropuerto station, impressive mural about people from all the countries) and Nuevos Ministerios (big mural about Madrid and other works of art). Change there to line L10 and go to Chamartín (new big mezzanine for the L1 extension), Alonso Martínez (walk north to the historic Andén 0 Chamberí underground station which has been turned into a museum), Príncipe Pio (built under the Norte railway station, with nice views of the old station). Change there to line L2 and go to Retiro (nice station with tile murals by Mingote).
Andén 0 Chamberí. The goal is showing the public a little piece of underground life in the capital at the start of the 20th century. The museum consists of a restored metro station by architect Antonio Palacios, abandoned in 1966. Old ticket counters and gates and old ceramic advertisements are still present, videos are on display. The museum has a branch at the Engine Shed at calle Valderribas, 49 near Pacífico metro station. Since 2008. Location: Abandoned Chamberí metro station from 1919. Address: Corner of Calle de Luchana and Calle de Sta Engracía. At Iglesia, Bilbao, Rubén Darío metro station. Hours (check before visiting): Thu 10am to 1pm, Fri 11am to 7pm, Sat+Sun 11am to 3pm. Admission: free. Reference: metromadrid.es (official website). notesfrommadrid.com, typicallyspanish.com, esmadrid.com.
The remodelling of stations led to the discovery of major archaeological and palaeontological findings, now turned into museums and open to the public, like the Caños del Peral Museum at Ópera or the paleontological site at Carpetana station. 
Exhibits in stations:
Carpetana: This is a significant site for paleontological remains in the suburban region. When installing elevators at the station in 2008, experts found over 5,000 animal remains of a wide range of genuses, dating from the Middle Miocene period (about 14 million years ago). Replicas of some of the fossils were installed, thus converting the station into a downright museum, including explanatory boards and showcases with replicas of the flora and fauna that once inhabited the place.
Opera: The station houses the Caños del Peral archaeological museum (230 square metres), featuring audiovisual displays, a 16th century fountain and other water supply works discovered during the station remodelling works in 2008, such as the “Arenal Sewer”.
Cercanias lines C2, C3, and C10 have express trains called Civis, inbound in the morning and outbound in the afternoon. On light rail line ML3 between Boadilla and Madrid, some trains skip the underused stops in between.
Buzzing before departure. Before arriving to the station, a recorded announcement says: "Próxima estación [name], correspondencia con línea [number]". This is Castilian and means: "Next station [name], transfer with line [number]". Sometimes, especially in old stations on line 1 they have also this text: "Próxima estación: Tirso de Molina. ¡Atención! Estación en curva, al salir tengan cuidado de no introducir el pie entre coche y andén", which means: "Next station: Tirso de Molina. Attention! Station is in a curve; while you get off the train, mind your step, don't step between the train and the platform." Line 6 and 7 have older trains and those have a whistle sound when the doors close.