There's more gravitational force in our galaxy (and others) than can be explained by counting stars made of ordinary matter. So why not lots of dark planetary systems (i.e., without stars) made of ordinary matter? Why must we assume some undiscovered and unexplained form of matter?
There is a very precise reason why dark planets made of 'ordinary matter' (baryons - particles made up of 3 quarks) cannot be the dark matter. It turns out that the amount of baryons can be measured in two different ways in cosmology:


By measuring present-day abundances of some light elements (esp deuterium) which are very sensitive to the baryon amount.
By measuring the distribution of the hot and cold spots in the Cosmic Microwave background (CMB), radiation left over from the early universe that we observe today.


These two methods agree spectacularly, and both indicate that baryons are 5% of the total stuff (energy/matter) in the universe.  Meanwhile, various measures of gravitational clustering (gravitational lensing, rotation of stars around galaxies, etc etc) all indicate that total matter comprises 25% of the total. (The remaining 75% is in the infamous dark energy which is irrelevant for this particular question). 

Since 5% is much less than 25%, and since the errors on both of these measurements are rather small, we infer that most of the matter, about 4/5 ths (that is, 20% out of 25%) is 'dark' and NOT made up of baryons. 
