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 and ≈1.6 Gyr and rotation periods between ≈1 and 12.4 days have been observed. We use the X-ray spectra to derive coronal element abundances of C, N, O, Ne, Mg, Si, S, and Fe and the coronal emission measure distribution (EMD). We find that 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. This transformation is coincident with a steep decline of nonthermal radio emission. The results are in qualitative agreement with a simple model in which the stream of electrons in magnetic fields suppresses diffusion of low-FIP ions from the chromosphere into the corona. The coronal emission measure distributions 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^-α, as previously found for solar and stellar flares. We obtain the relevant power-law index α from the slope of the high-temperature tail of the EMD. Our EMDs indicate α ≈ 2.2-2.8, in excellent agreement with values previously derived from light curves of magnetically active stars. Modulation with timescales reminiscent of flares is found in the light curves of all our targets. Several strong flares are also observed. We use our α-values to simulate light curves and compare them with the observed light curves. We thus derive the range of flare energies required to explain the light-curve modulation. More active stars require a larger range of flare energies than less active stars within the framework of this simplistic model. 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.