Single-molecule Förster resonance energy transfer (FRET) experiments are an important method for probing biomolecular structure and dynamics. The results from such experiments appear to be surprisingly independent of the excitation power used, in contradiction to the simple photophysical mechanism usually invoked for FRET. Here we show that excited-state annihilation processes are an essential cause of this behavior. Singlet-singlet annihilation (SSA) is a mechanism of fluorescence quenching induced by Förster-type energy transfer between two fluorophores while they are both in their first excited singlet states (S1S1), which is usually neglected in the interpretation of FRET experiments. However, this approximation is only justified in the limit of low excitation rates. We demonstrate that SSA is evident in fluorescence correlation measurements for the commonly used FRET pair Alexa 488/Alexa 594, with a rate comparable to the rate of energy transfer between the donor excited state and the acceptor ground state (S1S0) that is exploited in FRET experiments. Transient absorption spectroscopy shows that SSA occurs exclusively via energy transfer from Alexa 488 to Alexa 594. Excitation-power dependent microsecond correlation experiments support the conclusion based on previously reported absorption spectra of triplet states that singlet-triplet annihilation (STA) analogously mediates energy transfer if the acceptor is in the triplet state. The results indicate that both SSA and STA have a pronounced effect on the overall FRET process and reduce the power dependence of the observed FRET efficiencies. The existence of annihilation processes thus seems to be essential for using FRET as a reliable spectroscopic ruler at the high excitation rates commonly employed in single-molecule spectroscopy.