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LaTiO₃, a 3d transition metal oxide, has been of interest for its prototypical Mott insulator character, and can be readily tuned by excess oxygen doping from the insulating to the metallic phase. In this study, metallic thin films of LaTiO₃ of different thicknesses (3, 5 and 10u.c.) grown by pulsed laser deposition on SrTiO₃ substrates are investigated and show a series of very interesting transport effects. The films show metallic behavior, high carrier densities of ~ 2x10²³ cm^-3 and transport mobilities of μ > 40 000cm² /V.s at low T. Under a perpendicular magnetic field, a strong non-saturating colossal magnetoresistance (CMR) develops with amplitudes up to 6500%. Moreover, this MR is observed to be linear starting from very low field (<1T) and non-saturating up to at least 11T. This very distinct feature is compatible with the existence of low-mobility islands with a coverage of up to 88%. The presence of so many islands under magnetic field in an otherwise high mobility system at zero magnetic field, hints to a possible paramagnetic nature of the islands. On top of these findings, an in-plane anisotropic magnetoresistance (AMR) and a planar Hall effect (PHE) is observed.