Solid-state photodetectors have several distinctive features making them suitable for many applications in scintillation detection. However, unity-gain devices such as silicon PIN or mercuric iodide photodiodes show relatively poor timing performance as compared to photomultiplier tubes, especially for sub-MeV energy radiation. Avalanche photodiodes (APDs) have an internal gain which enables significantly better timing capabilities. The purpose of this work is to investigate the potential of avalanche photodiodes for timing discrimination with five types of scintillators, organic and inorganic, spanning a wide range of conditions in terms of decay time constant, wavelength of emission and signal amplitude. Silicon APDs of reach-through structure with a 5 x 5 mm2 active area have been used for the measurements. All scintillators were 4 x 4 x 4 mm3 in dimensions and optimized for light collection. Results show that for the 511 keV annihilation radiation, timing as fast as 1.4 ns is achieved with fast organic scintillators and well below 10 ns FWHM for the most common inorganic scintillators such as NaI(T1), CsI(T1) and BGO. All measurements were performed at room temperature.