Aims. The development of a general code for 3D Ly\alpha radiation transfer in galaxies to understand the diversity of Ly\alpha line profiles observed in star-forming galaxies and related objects. Methods. Using a Monte Carlo technique, we developed a 3D Ly\alpha radiation transfer code that allows for prescribed arbitrary hydrogen density, ionisation, temperature structures, dust distributions, arbitrary velocity fields, and UV photon sources. As a first test and application we examined the Ly\alpha line profiles predicted for several simple geometrical configurations and their dependence on the main input parameters. Results. Overall, we find line profiles reaching from doubly peaked symmetric emission to symmetric Voigt (absorption) in static configurations with increasing dust content, and asymmetric red- (blue-) shifted emission lines with a blue (red) counterpart ranging from absorption to emission (with increasing line/continuum strength) in expanding (infalling) media. In particular we find the following results to be interesting for the interpretation of Ly\alpha profiles from galaxies. 1) Standard Ly\alpha absorption line fitting of global spectra of galaxies may lead to an underestimation of the true hydrogen column density in certain geometrical conditions; 2) Normal (inverted) P-Cygni-like Ly\alpha profiles can be obtained in expanding (infalling) media from objects without any intrinsic Ly\alpha emission, as a natural consequence of radiation transfer effects; 3) The formation and the detailed shape of Ly\alpha profiles resulting from expanding shells has been thoroughly revised. In particular we find that, for sufficiently large column densities ( N_{\rm H} \ga 10cm super(-2)), the position of the main Ly\alpha emission peak is quite generally redshifted by approximately twice the expansion velocity. This is in excellent agreement with the observations of z \sim 3 LBGs, which show that Ly\alpha is redshifted by similar to 2V_{\rm exp}, where V_{\rm exp} is the expansion velocity measured from the interstellar absorption lines blueshifted with respect to the stellar redshift. This finding also indicates that large- scale, fairly symmetric shell structures must be a good description of the outflows in LBGs.