We present the results of photometric observations of 1996 FG3, 1998 PG, and (5407) 1992 AX. Each asteroid has a complex lightcurve that can be described as the coaddition of two independent components, one with a short synodic period P1 of several hours, and another with a longer synodic period P2. For 1996 FG3, the shape of the long-period component strongly suggests a system of two bodies in bound orbits about their common center of mass, displaying both mutual eclipses and mutual occultations. We estimate the following parameters of the binary system: the primary's rotation period is P1=(3.5942±0.0002) h, the system's orbital period is P2=(16.135±0.005) h, the system's semimajor axis a=(1.7±0.3) dp, the eccentricity is 0.05±0.05, and the secondary-to-primary diameter ratio ds/dp=0.31±0.02. The measured color indices suggest that 1996 FG3 belongs to the C taxonomic class; assuming the geometric albedo p=0.06 typical for the class, we estimate the diameter of the primary dp=1.4 km. For 1998 PG and (5407), the evidence for binary systems is less conclusive. However, assuming a binary model, we estimate that both systems have a secondary-to-primary diameter ratio ds/dp≥0.3. For 1998 PG, the primary and secondary rotation periods are P1=(2.51620± 0.00003) h and 2P2=(14.007±0.0014) h, respectively. (If the secondary's rotation is tidally coupled to the orbital motion, the latter is also the system's orbital period.) For (5407), the primary's rotation period is P1=(2.54878±0.00007) h, and the orbital period is 2P2=(13.5196±0.0016) h. The color indices of 1998 PG are consistent with an S classification. Assuming p=0.16, the primary's diameters are dp=0.9 and 4.0 km for 1998 PG and (5407), respectively. The finding of the three objects doubles the known sample of probable/possible binary asteroids. The six known objects are so similar in some of their characteristics that we expect that most or all of them have been formed by the same mechanism, such as the tidal disruptions during close encounters with Earth proposed by Bottke and Melosh (Nature281, 51, 1996). The population of binary asteroids among small, especially near-Earth, asteroids seems to be significant. Our new observations support an earlier estimate that 17% of NEAs are binary (uncertainty factor of 2).