  (abridged) Infrared selection is a potentially powerful way to identify
heavily obscured AGN missed in even the deepest X-ray surveys. Using a 24
micron-selected sample in GOODS-S, we test the reliability and completeness of
three infrared AGN selection methods: (1) IRAC color-color selection, (2) IRAC
power-law selection, and (3) IR-excess selection; we also evaluate a number of
infrared excess approaches. We find that the vast majority of non-power-law
IRAC color-selected AGN candidates in GOODS-S have colors consistent with those
of star-forming galaxies. Contamination by star-forming galaxies is most
prevalent at low 24 micron flux densities (~100 uJy) and high redshifts (z~2),
but the fraction of potential contaminants is still high (~50%) at 500 uJy, the
highest flux density probed reliably by our survey. AGN candidates selected via
a simple, physically-motivated power-law criterion (PLGs), however, appear to
be reliable. We confirm that the infrared excess methods successfully identify
a number of AGN, but we also find that such samples may be significantly
contaminated by star-forming galaxies. Adding only the secure Spitzer-selected
PLG, color-selected, IR-excess, and radio/IR-selected AGN candidates to the
deepest X-ray-selected AGN samples directly increases the number of known X-ray
AGN (84) by 54-77%, and implies an increase to the number of 24 micron-detected
AGN of 71-94%. Finally, we show that the fraction of MIR sources dominated by
an AGN decreases with decreasing MIR flux density, but only down to f_24 = 300
uJy. Below this limit, the AGN fraction levels out, indicating that a
non-negligible fraction (~10%) of faint 24 micron sources (the majority of
which are missed in the X-ray) are powered not by star formation, but by the
central engine.
