(abridged) We investigate the long-term evolution of X-ray coronae of solar analogs based on high-resolution X-ray spectroscopy and photometry with XMM-Newton. Six nearby main-sequence G stars with ages between ~0.1 Gyr and \~1.6 Gyr and rotation periods between ~1d and 12.4d have been observed. We derive coronal element abundances and the coronal emission measure distribution (EMD). The abundances change from an inverse-First Ionization Potential (FIP) distribution in stars with ages around 0.1 Gyr to a solar-type FIP distribution in stars at ages of 0.3 Gyr and beyond. The coronal EMDs show shapes characterized by power-laws on each side of the EMD peak. The latter shifts from temperatures of about 10 MK in the most rapidly rotating, young stars to temperatures around 4 MK in the oldest target considered here. The power-law index on the cooler side of the EMD exceeds expected slopes for static loops, with typical values being 1.5-3. We interpret this slope with a model in which the coronal emission is due to a superposition of stochastically occurring flares, with an occurrence rate that is distributed in radiated energy E as a power-law, dN/dE ~ E^-a. Our EMDs indicate a ~ 2.2-2.8, in excellent agreement with values previously derived from light curves of magnetically active stars. We derive the range of flare energies required to explain the light-curve modulation. In an overall scenario, we propose that flaring activity plays a larger role in more active stars. In this model, the higher flare rate is responsible both for the higher average coronal temperature and the high coronal X-ray luminosity, two parameters that are indeed found to be correlated.