How do we know Dark Matter is non-baryonic? It seems widely stated, but not thoroughly explained, that Dark Matter is not normal matter as we understand it. Wikipedia states "Consistency with other observations indicates that the vast majority of dark matter in the universe cannot be baryons, and is thus not formed out of atoms."
How can we presume to know this? Our best evidence for such dark matter is the rotational speeds of galaxies. It sounds like we can measure/approximate the gas density and stellar masses somehow, yet I don't understand how we can account for things like planets, asteroids, black holes without accretion disks, and other things that have mass but don't glow. How is it we dismiss these explanations for it, and jump right to WIMPs and other exotic explanations?
 A: Definitely see the comments on your question.  But a very brief outline of the data:
Rotation-curves and galaxy-cluster mass measurements show the detailed distribution of matter in those objects, the amount of mass far exceeds the observed mass ---> most mass is non-observed
Gravitational-lensing searches show that the "dark-matter" constituents must be composed of objects less than about $10^{-7} \textrm{ M}_\odot \sim 0.03 \textrm{ M}_\oplus$, i.e. it must be asteroid size or smaller.  Asteroid size can't really form stably (in such large amounts), and would be rapidly accreted by larger mass objects --> dark-matter constituents must be small.
Baryonic matter which is massive and small is constrained to gas and dust.  Both of these things, when hot, are easily observable (especially in hot galaxy clusters)... yet the premise is that we can't see them --> dark matter is not baryonic
There is lots more evidence, this is just the most basic outline.
The biggest additional piece overall is from cosmology: anisotropies in the cosmic microwave background tell you a lot about the initial universe and the seeds of structure formation -- comparing that with what we see in the current universe tells us about the evolution of structure in the universe, which ends up requiring that the dominant component of mass in the universe has no pressure which again rules out baryonic material. 
There's still more evidence.... but I'm not expert enough to try to explain it.
