We have performed the first single-particle spectroscopic measurements on individual graphene quantum dots (GQDs) and revealed several intriguing fluorescent phenomena that are otherwise hidden in the optical studies of ensemble GQDs. First, despite noticeable differences in the size and the number of layers from particle to particle, all of the GQDs studied possess almost the same spectral lineshapes and peak positions. Second, GQDs with more layers are normally brighter emitters but are associated with shorter fluorescent lifetimes. Third, the fluorescent spectrum of GQDs was red-shifted upon being aged in air, possibly due to the water desorption effect. Finally, the missing emission of single photons and stable fluorescence without any intermittent behavior were observed from individual GQDs.