Three-dimensional simulations of bubble formation in Newtonian and non-Newtonian fluids through a microchannel T-junction are conducted by the volume-of-fluid method. For Newtonian fluids, the critical capillary number Ca for the transition of the bubble breakup mechanism is dependent on the velocity ratio between the two phases and the microchannel dimension. For the power law fluid, the bubble diameter decreases and the generation frequency increases with higher viscosity parameter K and power law index n. For a Bingham fluid, the viscous force plays a more important role in microbubble formation. Due to the yield stress (y), a high-viscous region is developed in the central area of the channel and bubbles deform to a flat ellipsoid shape in this region. The bubble diameter and generation frequency are almost independent of K.