Is it at all possible that our current understanding of gravity could be wrong? Can the properties of gravity be altered to explain away the existence of dark matter?
That is the possibility that the alternative theories use. So far none of them quite manage to explain everything, but neither does dark matter.
http://www.world-science.net/othernews/070802_darkmatter.htm
In fact in a recent edition of New Scientist there was an interview with Mordehai Milgrom (the leading proponent of MoND theory) in which he suggested it was time to give up on dark matter. He suggests that applying Tensor-Vector-Scalar gravity theory allows it to work with General Relativity and can explain things like gravitational lensing.
So the state of play at the moment is that dark matter/dark energy is the popular theory, but alternative theories exist.