I guess the only really important thing is, the dark matter debate seems to have been really seriously tipped by the
bullet cluster observation from 2006. In that case an astronomical observation was made which astronomers consider to have been an actual direct observation of dark matter.
In the bullet cluster, two galaxies were seen to collide. When the two galaxies collided, the normal matter in the galaxies slowed down as it all collided with each other, but the dark matter in each galaxy just kept going. The dark matter in this case cannot be anything that interacts, or else it would have been caught up in the collision too. And it can't interact with or emit light, because we can't see it. But it must be
there, since we can observe its presence by the gravitational lensing it causes. And it must be "stuff"-- matter, I guess-- because it behaves like it, because it was traveling along with the galaxies until they collided and the dark matter was flung out. So this seems to demonstrate there is
something which acts like matter but interacts only by the gravitational force. Since nothing in the standard model fits this description, it must be that we will need to extend the standard model to accommodate it. (One interesting thing to look up here is the
minimal dark matter model, which shows us that we don't need to extend the standard model
much!) This observation seems to have convinced almost all physicists that dark matter is explained by some specific kind or kinds of as-of-yet unobserved particle.
I personally have confused philosophical issues with the whole dark matter idea (it's practically everywhere, right? so where is it? shouldn't there be, like, some
here, like in the solar system?), but I don't see any other way to explain the bullet cluster data.