I know that there's a lot of evidence for extremely compact bodies. But is there any observation from which we can infer the existence of an actual horizon?
Even if we are able to someday resolve directly the "shadow" of a possible black hole, isn't it still possible that it's just a highly compact body that's just gravitationally redshifting any radiation that it emits to beyond the detection capability of our telescopes? What would be indisputable evidence for a causal horizon?
Answer
At the galactic center, there is an object called Sagittarius A* which seems to be a black hole with 4 million solar masses. In 1998, a wise instructor at Rutgers made me make a presentation of this paper
http://arxiv.org/abs/astro-ph/9706112
by Narayan et al. that presented a successful 2-temperature plasma model for the region surrounding the object. The paper has over 300 citations today. The convincing agreement of the model with the X-ray observations is a strong piece of evidence that Sgr A* is a black hole with an event horizon.
In particular, even if you neglect the predictions for the X-rays, the object has an enormously low luminosity for its tremendously high accretion rate. The advecting energy is pretty "visibly" disappearing from sight. If the object had a surface, the surface would heat up and emit a thermal radiation - at a radiative efficiency of 10 percent or so which is pretty canonical.
Of course, you may be dissatisfied by their observation of the event horizon as a "deficit of something". You may prefer an "excess". However, the very point of the black hole is that it eats a lot but gives up very little, so it's sensible to expect that the observations of black holes will be via deficits. ;-)
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