Triplet-triplet annihilation (TTA) is studied in a wide range of fluorescent host:guest emitter systems used in organic light-emitting devices (OLEDs). Strong TTA is observed in host:guest systems in which the dopant has a limited charge-trapping capability. On the other hand, systems in which the dopant can efficiently trap charges show insignificant TTA, an effect that is due, in part, to the efficient quenching of triplet excitons by the trapped charges. Fluorescent host:guest systems with the strongest TTA are found to give the highest OLED electroluminescence efficiency, a phenomenon attributed to the role of TTA in converting triplet excitons into additional singlet excitons, thus appreciably contributing to the light output of OLEDs. The results shed light on and give direct evidence for the phenomena behind the recently reported very high efficiencies attainable in fluorescent host:guest OLEDs with quantum efficiencies exceeding the classical 25% theoretical limit.