We compute theoretical nova rates as well as type Ia SN rates in galaxies of different morphological type (Milky Way, ellipticals and irregulars) by means of detailed chemical evolution models, and compare them with the most recent observations. The main difference among the different galaxies is the assumed history of star formation. In particular, we predict that the nova rates in giant ellipticals such as M87 are 100-300 nova/yr, about a factor of ten larger than in our Galaxy (25 nova/yr), in agreement with very recent estimates from HST data. The best agreement with the observed rates is obtained if the recurrence time of novae in ellipticals is assumed to be longer than in the Milky Way. This result indicates that the star formation rate in ellipticals, and in particular in M87, must have been very efficient at early cosmic epochs. We predict a nova rate for the LMC of 1.7 nova/yr, again in agreement with observations. We compute also the K- and B-band luminosities for ellipticals of different luminous mass and conclude that there is not a clear trend for the luminosity specific nova rate with luminosity among these galaxies. However, firm conclusions about ellipticals cannot be drawn because of possible observational biases in observing these objects. The comparison between the specific nova rates in the Milky Way and the LMC indicates a trend of increasing nova rate passing from the Galaxy towards late-type spirals and Magellanic irregulars.