Context. The atmosphere of Earth-like extrasolar planets orbiting different types of stars is influenced by the spectral dependence of the incoming stellar radiation. The changes in structure and composition affect atmospheric radiation, hence the spectral appearance of these exoplanets. Aims. We provide a thorough investigation of infrared radiative transfer in cloud-free exoplanets atmospheres by not only analyzing the planetary spectral appearance but also discussing the radiative processes behind the spectral features in detail and identifying the regions in the atmosphere that contribute most at a given wavelength. Methods. Using cloud-free scenarios provided by a one-dimensional radiative-convective steady-state atmospheric model, we computed high-resolution infrared transmission and emission spectra, as well as weighting functions for exoplanets located within the habitable zone of F, G, K, and M stars by means of a line-by-line molecular absorption model and a Schwarzschild solver for the radiative transfer. The monochromatic spectra were convolved with appropriate spectral response functions to study the effects of finite instrument resolution. Results. Spectra of the exoplanets of F, G, K, and M stars were analyzed in the 4.5 μm N2O band, the 4.3 μm and 15 μm CO2 bands, the 7.7 μm CH4 band, the 6.3 μm H2O band, and the 9.6 μm O3 band. Differences in the state of the atmosphere of the exoplanets clearly show up in the thermal infrared spectra; absorption signatures known from Earth can be transformed to emission features (and vice versa). Weighting functions show that radiation in the absorption bands of the uniformly mixed gases (CO2, CH4, N2O) and (to some extent) ozone comes from the stratosphere and upper troposphere, and also indicate that changes in the atmospheres can shift sources of thermal radiation to lower or higher altitudes. Molecular absorption and/or emission features can be identified in the high-resolution spectra of all planets and in most reduced resolution spectra. Conclusions. Insight into radiative transfer processes is essential for analyzing exoplanet spectral observations; for instance, understanding the impact of the temperature profile (nb. non-existence of an inversion) on the CO2 bands facilitates their interpretation and can help avoid false positive or negative estimates of O3. The detailed analysis of the radiation source and sink regions could even help give an indication about the feasibility of identifying molecular signatures in cloud-covered planets, i.e. radiation mainly coming from the upper atmosphere is less likely to be hidden by clouds. Infrared radiative transfer and biomarker detectability in cloud-covered exoplanets will be presented in a companion paper.