Dark Matter 

So Vrot ~ constant over the disk of the Galaxy. This should confuse the hell out of you. 

Things to ponder:

Note that our galaxy isn't the only one that does this. Here is a compendium of rotation curves from Sofue (1999):

Look at the dynamical mass:

So as we go further and further out in the galaxy, there is more and more mass. And we don't see it. This is the Milky Way's dark matter halo.

How far out does it go? 100s of kpc? And there's a lot of stuff out there.

So 90% of the Milky Way's mass is invisible dark matter. Whoa....

So what could the dark matter be?