We present detailed predictions for the possible outcome of surveys of extragalactic sources soon to be carried out with the forthcoming generation of both ground based and satellite-borne telescopes, over the full range from near-IR to mm wavelengths. Estimates of the confusion limits, due both to stars and galaxies, for several particularly interesting wavebands have been worked out. Predictions for the near- and IR bands are based on up-to-date models for chemical and photometric evolution of early- and late-type galaxies, and allow for luminosity evolution of Seyfert nuclei. These models are shown to provide a good fit to the recent deep counts in the K band; they imply that E/S0 and spiral galaxies are present in roughly equal numbers for K less-than-or-equal-to 19. At fainter magnitudes spirals dominate; ground based surveys down to K = 21 would allow to test photometric evolution models up to z congruent-to 1 - 3. Deep surveys at longer wavelengths, requiring for example a few hour exposures with the most sensitive filters of the ISO camera, such as that centered at lambda = 6.7-mu-m, are particularly well suited for studying the photometric evolution of E/S0 galaxies at high redshift. We argue that relatively shallow surveys at the same lambda-over an area of a few square degrees would be particularly effective in providing an unbiased sample of low luminosity AGNs. Predictions for 25-mu-m less-than-or-equal-to lambda less-than-or-equal-to 1.3 mm are obtained by extrapolating a model fitting the IRAS deep survey data. The adopted dust emission spectrum from a few microns to 1.3 mm takes into account simple but realistic size and temperature distributions of grains and of PAH molecules. Surveys at lambda > 100-mu-m (i.e. beyond the dust emission peak) would allow to investigate dust reradiation from distant and primeval galaxies. For example, a survey at 800-mu-m with a flux limit of 30 mJy would have a strong likelihood of discovering actively star forming galaxies at z congruent-to 5, if they exist. The measurements of the diffuse background spectrum and intensity being carried out by COBE, will provide important constraints but will require a delicate subtraction of foreground emissions.
