Ancient Roman Forum - while it is not free to go into the Ancient Roman Forum, its free to look at and observe the ruins from the outside.  Walking down the Via dei Fiori Imperiali you will see the ruins of Trajan's Forum on your left while on your right you see a sloping hill going up towards the side of the Roman Forum; you can take this hill for a good vantage point of the forum or go to the Campidoglio, the plaza at the top of the Capitoline Hill and view the ruins - excellent place to take photos of the ruins

It's full of ruins, including aqueducts, mausoleums, temples, castles and several catacombs - all of these you do have to pay for but the walk is of course free and very worthwhile

Rome's non-Catholic cemetery, resting place for Keats and Shelley

from Piazza Navona to Piazza Barberini and beyond

Bramante's Tempietto (first temple of the High Renaissance) and amazing panoramic views of Roma

where Caesar was killed

Piazza della Bocca della Verità, 18, 00186 Roma RM, Italy

vHistoric building in south Rome, Square Colosseum

peep through the keyhole and see St Peter's perfectly framed at the end of a hedge lined avenue

Porta San Paolo and the Protestant Cemetery, Via Raffaele Persichetti, 00153 Roma RM

Top of the Spanish Steps is the Church of Trinita dei Monti - frescoes, astralobe, duo of anamorphoses (paintings which change perspective depending on where you are standing)

will have to queue, Michelangelo's Pietra & Bernini's baldachin (altar canopy)

When we visited it was still free to enter, this may have to changed but if it has and you have to pay an entrance free, it is exceptionally worthwhile to do so

Trevi Fountain is a gorgeous piece of Baroque (and Rococco) art, right in the centre of Rome.

Rome's most famous park which is free to visit and enjoy 

The dominating building in Palazzo Venezia which has incredible views of Rome, and if you are lucky the elevator ride to the viewing terrace is free and there are interesting exhibits inside the building to appreciate