The distribution of the orbits of close-in exoplanets shows evidence for ongoing removal and destruction by tides. Tides raised on a planet's host star cause the planet's orbit to decay, even after the orbital eccentricity has dropped to zero. Comparison of the observed orbital distribution and predictions of tidal theory shows good qualitative agreement, suggesting tidal destruction of close-in exoplanets is common. The process can explain the observed cutoff in small semimajor axis values, the clustering of orbital periods near three days, and the relative youth of transiting planets. Contrary to previous considerations, a mechanism to stop the inward migration of close-in planets at their current orbits is not necessarily required. Planets nearing tidal destruction may be found with extremely small semimajor axes, possibly already stripped of any gaseous envelope. The recently discovered CoroT-7 b may be an example of such a planet and will probably be destroyed by tides within the next few Gyrs. Also, where one or more planets have already been accreted, a star may exhibit an unusual composition and/or spin rate.