What keeps galaxies united like a solar system? Blackholes may be really strong but they act in a very short range. For example if the sun was a black having the same mass, it will be dark but we will still be revolving around it. It wont engulf us.
Also I hear that the outer stars in a galaxy rotates around the galaxy with same speed as the inside stars? This defies the law of gravity. Is this still a mystery? Does anybody know what is the pull on a star by a galaxy? And is this pull uniform throughout the galaxy?
Related Question:  Is there evidence of dark matter in our galaxy?
 A: Welcome to the mystery of Dark Matter.  The gravitational influence of an undetected (aside from its gravitational influence) amount of matter is what is causing the irregular rotation of stars in the galaxy as you noted (not black holes).  And solar systems behave much more classically, which again gave us the clue to dark matter's influence.
Wikipedia has a great run down on the history of how we figured out that dark matter is out there.  The most charming part of the story is about Vera Rubin getting stuck in an "unexciting" field of study because she wanted to raise a family.  Although Fritz Zwicky posited dark matter as early as 1933.  And it goes just beyond the rotation of stars in the galaxy, but also is apparent via gravitational lensing.
While you mention black holes, they are not it.  Black holes are indeed one of the more well known gravitational supermen of the universe, they do not make up enough of the universe (or galaxy) to account for the dark matter, which seems much more "cloud" like.
The pull is not totally uniform though.  We have created a sort of 3D map of dark matter in the universe by observing its effects on the visible matter.  And keep in mind, dark matter is a sort of placeholder name for this non-baryonic matter.  We are still trying to figure it out.
A: Dark matter is only the "caboose" on a whole train of answer.
When one object totally dominates the gravitational field of some interacting bodies, like the Sun does in the Solar System since it has 99% of the mass, all the objects orbiting the big one can be reasonably approximated as interacting with the central body. This is called the Two-body problem. In the two-body problem, both the angular and linear velocities decrease for objects in circular orbits as the orbital radius increases. In other words, Venus' year is longer than Mercury's, Earth's is longer than Venus', etc. Also, [CORRECTION:] Mercury literally flies through space at greater miles per hour than Venus, etc.
Now, a galaxy's central black hole is the most massive single object in the galaxy, but it is typically only a tiny fraction of the total mass. The mass of a galaxy is dominated by the overall soup of matter reaching out from the center. Since this is not the two-body problem, the Solar System results need not apply. To solve for how objects should behave in a soup, you basically consider just the amount of soup between your given object and the center. Therefore, objects farther out are basically behaving as if they are orbiting a more massive body than objects closer in.
The net result of that is that objects orbiting in a soup should have their angular and linear velocities decrease less than the traditional two-body problem. In fact, we observe that their linear velocities seem to be almost perfectly the same. That means there must be a lot of matter in the soup...
However, we can't find enough light-emitting, ordinary matter to account for how much matter we just inferred was there. This is the first and only part of the story where we need to invoke dark matter.
MOND is a theory that attempts to resolve this final discrepancy in a different way. Instead of inferring lots of mysterious matter of unknown properties, it modifies the math surrounding very slow gravitational interactions (technically, those involving very low accelerations). This math works extremely well, but it hasn't achieved widespread acceptance because there is no "story" or explanation backing up the math at all, and MOND is difficult or impossible to mesh with other, established theories like Special and General Relativity.  
A: This layman's answer:
In Newtonian physics, we generally simplify the problem of multiple bodies down to 2 points, as you pointed out yourself. But it's important to remember to take all the bodies into account when making this simplification.
A star at the outer edge of a galaxy is pulled not only by the supermassive black hole in the center, but also by all the other stars in the galaxy. Each one's effect is pretty small, but together they're pulling strong enough to keep the edge star confined.
In other words, if all the stars in a galaxy except one at the edge suddenly disappeared and the black hole at the center didn't change in any significant way then it would be likely that the star would just fly away!
As for the outer stars' speed - it's not necessarily the case that dark matter is involved. There are some explanations that claim good old Newtonian physics account for that (e.g. http://www.starpulls.com/Galaxy.htm ). I'll leave this one to someone more experienced, though.
