We present the observation of critical coupling in a high- Q fused-silica microsphere whispering-gallery mode resonator coupled to a fiber taper. Extremely efficient and controlled power transfer to high- Q ( approximately 10(7)) resonators has been demonstrated. Off-resonance scattering loss was measured to be less than 0.3%. On-resonance extinction in transmitted optical power through the fiber coupler was measured as high as 26 dB at the critical coupling point. This result opens up a range of new applications in fields as diverse as near-field sensing and quantum optics.