If the photon emission (shown here as a short wavelength, that is downward pointing, "long" green line in the diagram) occurs between states of the same spin state (e.g. S1 ---> S0) this is termed fluorescence. If the spin state of the initial and final energy levels are different (e.g. T1 --> S0), the emission (loss of energy) is called phosphorescence. In the diagram this is depicted by a longer wavelength (lower energy) and therefore shorter length red line. Since fluorescence is statistically much more likely than phosphorescence for most molecules, the lifetimes of fluorescent states are very short (1 x 10-5 to 10-8 seconds) and phosphorescence somewhat longer (1 x 10-4 seconds to minutes or even hours; think about glow-in-the-dark flying disks).
Three nonradiative deactivation processes are also significant here: internal conversion (IC), intersystem crossing (ISC) and vibrational relaxation. Examples of the first two can be seen in the diagram. Internal conversion is the radiationless transition between energy states of the same spin state (compare with fluorescence-a radiative process). Intersystem crossing is a radiationless transition between different spin states (compare to phosphorescence). Vibrational relaxation, the most common of the three--for most molecules, occurs very quickly (<1 x 10-12 seconds) and is enhanced by physical contact of an excited molecule with other particles with which energy, in the form of vibrations and rotations, can be transferred through collisions. This means that most excited state molecules never emit any energy because in liquid samples the solvent or, in gas phase samples, other gas phase molecules that are present "steal" the energy before other deactivation processes can occur.
An animation detailing these processes is here.