LittleToe:
Numerous eyewitnesses, beginning two thousand years ago and continuing into the present time (with at least three or four on this thread). Many would suggest that eyewitness accounts precede this by several millenia, too, but that's an extended area of investigation.
Eyewitness accounts are notoriously unreliable, and certainly don't meet the standards Rex mentioned. Now, of course, there are a lot of eyewitness accounts, which would certainly be taken into account in a law court. If fifty people say they saw the same person committing a crime, then a conviction is likely, even without physical evidence. However, if fifty people all disagreed about who they saw committing the crime, and the details of when, where and how it happened, then their evidence would likely be dismissed. This analogy, I think, corresponds very well to experiences of the supernatural. While there are thousands of recorded incidents, many of them contradict one another. While some see the Virgin Mary, others are given evidence that Allah is the one true god, while others are abducted by aliens. Even those who encounter the same deity are often given different instructions.
This leaves several possibilities:
1. All (or many) of these experiences are real, and there are different competing deities.
2. All (or many) of the experiences are real, and there is one deity/entity or group of entities who are responsible for all of them.
3. All (or many) of the experiences involving one particular deity/entity are real, but the rest are delusions.
4. None of the experiences are real, all are coincidences or delusions.
(I can't think of any other possibilities, but would consider any that people can think of.)
Numbers one and two are, to me, essentially the same in that they require a certain dishonesty from the supernatural entities in question. Obviously, if people are seeing visions of Ganesh, then Allah's claim to be the one true god can't be true. While the idea of a pantheon of warring gods is no more ridiculous to me than many other supernatural claims, the idea of such gods each pretending to be the true one is. Similarly, the idea of some entities impersonating different deities for shits and giggles strikes me as unlikely.
Option three makes more sense to me. It's certainly the view many religious people would have. Jesus really appears to people, but visions of other gods are delusions (or tricks of the devil).
However, unless there is substantially more evidence for one claim than for any other, there's no obvious justification for making such a claim. It's telling that the Virgin Mary never appears in tortilla chips (or the local equivalent) in Saudi Arabia or that African tribal gods never appear in visions to Lutherans.
Which leaves us with option four, which you won't be surprised to hear, is my preferred explanation. Humans have evolved to live in small groups with no long-distance communication. As a result, our ideas of probabilities are based on this. Living in the modern world, we tend to underestimate the likelihood of certain events, leaving us amazed by coincidences that are not really that unlikely. We also have excellent pattern-recognition techniques, sometimes a little too good, which lead us to see patterns in random events. And finally, we are influenced in all sorts of ways by the culture in which we live.
So no, eyewitness testimony will not be enough for me, unless there is evidence to back it up. Rex claims he has some, so I'd like to see it.