Tidal disruption of stars by supermassive black holes at the centers of galaxies is expected to produce unique emission-line signatures, which have not yet been explored adequately. Here we report the discovery of extremely strong coronal lines from FeX up to FeXIV in a sample of seven galaxies (including two recently reported cases), which we interpret as such signatures. This is the first systematic search for objects of this kind, by making use of the immense database of the Sloan Digital Sky Survey. The galaxies, which are non-active as evidenced by the narrow line ratios, show broad emission lines of complex profiles in more than half of the sample. Both the high-ionization coronal lines and the broad lines are fading on timescales of years in objects observed with spectroscopic follow-ups, suggesting their transient nature. Variations of inferred non-stellar continua, which have absolute magnitudes of at least -16 to -18 mag in the g band, are also detected in more than half of the sample. The coronal line emitters reside in sub-Llow * disk galaxies (-21.3 < M sub(i) < -18.5) with small stellar velocity dispersions. The sample seems to form two distinct types based on the presence or absence of the FeVII lines, with the latter having relatively low luminosities of OIII, FeXI, and the host galaxies. These characteristics can most naturally be understood in the context of transient accretion onto intermediate-mass black holes at galactic centers following tidal disruption of stars in a gas-rich environment. We estimate the incidence of such events to be around 10 super(-5) yr super(-1) for a galaxy with -21.3 < M sub(i) < -18.5.