The Rossiter-McLaughlin (RM) effect is the distortion of stellar spectral lines that occurs during eclipses or transits, due to stellar rotation. We assess the future prospects for using the RM effect to measure the alignment of planetary orbits with the spin axes of their parent stars, and to confirm exoplanetary transits. We compute the achievable accuracy for the parameters of interest, in general and for the five known cases of transiting exoplanets with bright host stars. We determine the requirements for detecting the effects of differential rotation. For transiting planets with small masses or long periods (as will be detected by forthcoming satellite missions), the velocity anomaly produced by the RM effect can be much larger than the orbital velocity of the star. For a terrestrial planet in the habitable zone of a Sunlike star found by the Kepler mission, it will be difficult to use the RM effect to confirm transits with current instruments, but it still may be easier than measuring the spectroscopic orbit.
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