Dry reforming of methane (DRM) is an eco-friendly method of syngas production due to the utilization of two main greenhouse gases—methane and carbon dioxide. An industrial application of methane dry reforming requires the use of a catalyst with high activity, stability over a long time, and the ability to catalyze a reaction, leading to the needed a hydrogen/carbon monoxide ratio. Thus, the aim of the study was to investigate the effect of support and noble metal particles on catalytic activity, stability, and selectivity in the dry reforming process. Ni and Ni–Ru based catalysts were prepared via impregnation and precipitation methods on SiO2, ZrO2, Al2O3, and MgAl2O4 supports. The obtained catalysts were characterized using X-ray diffractometry (XRD), inductively coupled plasma optical emission spectrometry (ICP-OES), Brunauer–Emmett–Teller (BET) specific surface area, and elemental carbon-hydrogen-nitrogen-sulphur analysis (CHNS) techniques. The catalytic activity was investigated in the carbon dioxide reforming of a methane process at 800 °C. Catalysts supported on commercial Al2O3 and spinel MgAl2O4 exhibited the highest activity and stability under DRM conditions. The obtained results clearly indicate that differences in catalytic activity result from the dispersion, size of an active metal (AM), and interactions of the AM with the support. It was also found that the addition of ruthenium particles enhanced the methane conversion and shifted the H2/CO ratio to lower values.