Hmm. Table rapping seems like fraud to me, and many cases of fraud have been uncovered. However the ouija board thing is not fraud. It may be something like Hypnagogue says, a self-deception, but it isn't fraud.
Hypnagogue.
I'm not sure what serious objection you have. The explanation readily explains why one is typically surprised that the glass moves in a certain way, and why one thinks that it is not really him/herself doing it.
My serious objection is that I do not think the ideomotor effect explains what happens. As I say, I can't show that it's the wrong explanation, but in most instances when I have done it (and while being curious and I hope open-minded I'm by nature sceptical about such things) it is my conclusion that the pressure of fingers on the glass is not sufficient to account for the movement of the glass.
For instance, in the past I did this quite a few times with my mother. With just two people involved it is immediately obvious if someone is moving the glass with their finger, since it takes a certain pressure on the glass to do it. Of course it's possible that I'm wrong about this, and certainly if I hadn't done it so many times I would have happily assumed that the ideomotor effect was the solution. However given my experiences I don't think it is the solution. If it is then it should be very easy to prove it, and I'm not aware that it's been proved. Also, it's a pretty strange unconscious process that can spell out such messages as "The only way to eternal life is Holy communion" and sign it the Bishop of Bath and Wells.
In the case of the Ouji board, we are not aware of the thoughts which we presume are responsible for guiding our behavior, and we can only assume that the words we spell are somehow related to the contents of the subconscious thoughts of the board operators. (Perhaps a sufficiently sophisticated neuroscience could settle that matter for us in the future.)
Why do we have to assume this? Science should be about observations and experiment, not assumptions. If the ideomotor effect has not been shown to cause the movement of the glass then we don't know whether it does or does not.
One anecdote. At school I used to do this with some friends regularly over a period of a few months. For one four day period each time we started we got James Joyce on the line. That is, each time we asked who was there, the glass moved to spell out James Joyce. Now usually the movements of the glass are fairly weak, but this was different. Every now and again the glass would suddenly whizz energetically around the circle of letters until they were all knocked to the floor. If any of the three or four people doing it had been pushing or pulling the glass it would have been perfectly obvious, and when we tried to mimic this effect by pushing or pulling the glass ourselves we could not do it. (We were also suspicious about what was going on, and someone consciously or unconsciously moving the glass with their finger is the obvious solution). Perhaps we were wrong about this, but if so one of our subconscious minds speaks in very bad language, since it was all f**k this and f**k that in the messages the glass spelt out, as one would expect.
My brother, a little younger than me, also started to do it. However one time the glass spelt out 'Gabriel', and then it flew off the table and smashed in mid-air, since when he's absolutely refused to have anything more to do with it under any circumstances. (The incident happened over thirty years ago - but he still feels the same). But I wasn't there so have no comment on that incident. I'm only taking into account what has happened to me first hand.
If it is not yet know whether the ideomoter effect is responsible then there's not much point in our guessing. Still, it surprises me that it is not known to be responsible, since I would have thought it was fairly easy to design an experiment to test whether it is or not. I wouldn't want to argue about it with you except to say that I don't find this proposed solution convincing. It seems to be no more than a conjecture.
I don't have any axe to grind on this, perhaps its all got a perfectly ordinary explanation and is nothing to do with the 'other side'. If so fine, and it's what one would expect. But the ideomotor effect does not seem a plausible explanation to me.