We report photonic quantum circuits created using an ultrafast laser processing technique that is rapid, requires no lithographic mask and can be used to create three-dimensional networks of waveguide devices. We have characterized directional couplers--the key functional elements of photonic quantum circuits--and found that they perform as well as lithographically produced waveguide devices. We further demonstrate high-performance interferometers and an important multi-photon quantum interference phenomenon for the first time in integrated optics. This direct-write approach will enable the rapid development of sophisticated quantum optical circuits and their scaling into three-dimensions.