Piazza Navona in the Campus Martius, close to the Pantheon, has fountains by Bernini and della Porta. There was a dove convention going on apparently.
Trevi fountain, the biggest fountain in Rome, also by Bernini. There seems to always be a crowd.
Fontana delle Naiadi on the Piazza della Repubblica:
Fontana delle Tartarughe, Piazza Mattei, Sant’Angelo. The original fountain design called for four bronze dolphins on the upper vasque, supported by the upraised hands of the four ephebes. The four dolphins were removed because of issues with low water pressure, so the upraised hands of the statues seemed to have no purpose. Thus the turtles were later added.