The following restaurants all have a 'menu del dia' lunchtime meal for approximately 10 euros.
Special mention must go to restaurant at Circulo Bellas Artes - one to definitely avoid. I've often had a single dish in a menu that I haven't thought really worked - never have I not finished any of my three dishes. At 13 euros, it was also more expensive than any of the restaurants below.
If you prefer to explore by yourself than to follow my recommendations, check out my advice on How to Spot a Good Restaurant in Spain.
Thanks to La Cuchara for recommending some of these restaurants to me.
1. Con Dos Fogones
Quite simply one of the best meals I have ever had, in an funky, modern setting. The food was an excellent combination of traditional and fusion dishes (I had a cream of pumpkin soup and amazing duck with hummus), good staff, and very reasonably priced - just 10 euros!
Address: c/ San Bernadino, 9 (Metro: Plaza de España/Santo Domingo/Noviciados)
Large restaurant (there's always space) with fresh wooden deco in the heart of Chueca. Try the gazpacho.
Address: C/ Libertad, 21 (Metro: Chueca/Gran Via)
3. La Musa MalasañaModern restaurant with some excellent dishes, though choice is limited (usually only two options for each course).
Address: C/ Manuela Malasaña 18 (Metro: Bilbao)
4. La Buga del LoboColorful restaurant that's a short walk from the Reina Sofia modern art museum. Reasonably priced dishes in the evening too, but the best deals (as always) are to be had at lunchtime.
Address: c/Argumosa 11 (Metro: Lavapies/Atocha)
5. Restaurante Doña Juana
The most 'average' looking restaurant you'll find in Madrid, this place stands out because it serves Cocido Madrileño (traditional Madrid stew) every day (apart from Monday's when they're closed). They also have a menu del dia at weekends, which is rare.
Address: C/ Postigo de San Martin 5 (Metro: Callao)