We demonstrate a simple method for efficient coupling of standard single-mode optical fibers to a high-Q optical microsphere cavity. Phase-matched excitation of whispering-gallery modes is provided by an angle-polished fiber tip in which the core-guided wave undergoes total internal reflection. In the experimental setup, which included a microsphere with both an input and an output coupler, the total fiber-to-fiber transmission at resonance reached 23% (total insertion loss, 6.3 dB), with loaded quality factor Q greater than or equal to 3 x 10(7) and unloaded Q approximate to 1.2 x 10(8) at 1550 nm. A simple pigtailing method for microspheres permits their wider use in fiber optics and photonics devices. (C) 1999 Optical Society of America.