Ground-based searches for transiting Jupiter-sized planets have so far produced few detections of planets, but many of stellar systems with eclipse depths, durations, and orbital periods that resemble those expected from planets. I show that these detection rates are consistent with our present knowledge of binary and multiple-star systems, and of Jovian-mass extrasolar planets. Upcoming space-based searches for transiting Earth-sized planets will be largely unaffected by the sources of false alarms that afflict current ground-based searches, with one exception, namely distant eclipsing binaries whose light is strongly diluted by that of a foreground star. A byproduct of the rate estimation is evidence that the period distribution of extrasolar planets is depressed for periods between 5 and 200 days.
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