We report picosecond laser welding of similar and dissimilar materials based on plasma formation induced by a tightly focused beam from a 1030 nm, 10 ps, 400 kHz laser system. Specifically, we demonstrate the welding of fused silica, borosilicate, and sapphire to a range of materials including borosilicate, fused silica, silicon, copper, aluminum, and stainless steel. Dissimilar material welding of glass to aluminum and stainless steel has not been previously reported. Analysis of the borosilicate-to-borosilicate weld strength compares well to those obtained using similar welding systems based on femtosecond lasers. There is, however, a strong requirement to prepare surfaces to a high (10-60 nm Ra) flatness to ensure a successful weld.