We present kinematics and photometric evidence for the presence of seven candidate tidal dwarf galaxies in Stephan's Quintet. The central regions of the two most probable parent galaxies, NGC 7319 and NGC 7318B, contain little or no gas whereas the intragroup medium and, in particular, the optical tails that seem to be associated with NGC 7318B are rich in cold and ionized gas. Two tidal dwarf candidates may be located at the edge of a tidal tail, another located within a tail, and for the four others there is no obvious stellar/gaseous bridge between them and the parent galaxy. Two of the candidates are associated with H I clouds, one of which is, in addition, associated with a CO cloud. All seven regions have low continuum fluxes and high Halpha luminosity densities [F(Halpha) = (1-60) × 10-14 ergs s^-1 cm^-2]. Their magnitudes (M_B = 16.1 to 12.6), sizes (˜ 3.5 h₇₅ ^-1 kpc), colors (typically B R = 0.7), and gas velocity gradients (˜ 8 26 h₇₅ km s^-1 kpc^-1) are typical for tidal dwarf galaxies. In addition, the ratios between their star formation rates determined from Halpha and from the B-band luminosity are typical of other tidal dwarf galaxies. The masses of the tidal dwarf galaxies in Stephan's Quintet range from ˜ 2 × 10⁸ to 10¹⁰ M_&sun;, and the median value for their inferred mass-to-light ratios is 7 (M/L)_&sun;. At least two of the systems may survive possible `fallbacks' or disruption by the parent galaxies and may already be, or turn into, self-gravitating dwarf galaxies, new members of the group.