I absolutely recommend, above all others, Trattoria Luzzi on Via di San Giovanni in Laterano. 5 minutes walk from Colosseo Underground. Fantastic food, owned by a fantastic bloke and the food is outstanding. It's closed on Wednesdays.
Trattoria Quanto sei bella Roma on Via Selinute in Quadraro is worth a look. Need a taxi but again it's reasonably cheap and does fantastic Roman food.
La Zingarella on Via Gino Capponi in San Giovanni is worth a visit. It's a 5 minute walk from Furio Camillo underground station.
Pane, Vino e San Daniele in the Jewish ghetto is a 'chain' but does fantastic food.
TrentaDue on Via Volsci is a Leftist squat that does a lunch and dinner menu.
Ridiculously cheap, really good food and in a famous working-class district of Rome. It's a 10 minute walk from Termini station.