I've seen in documentaries that at the center of each galaxy is a super massive black hole which holds the galaxy together.
Since black holes have such a strong pull, are we slowly being pulled in closer and closer to this black hole?
That's not really how gravity works.
When a galaxy forms, all the dust that falls into it retains angular momentum round the centre (and this pattern repeats locally round stars, and round planets round those stars etc) which leads to the relatively stable structures we see today with spiral arms etc.
Collisions and near collisions can change the direction of stuff orbiting a centre, but we are quite far out, so while we could change orbits we would be as likely to move wider than closer in the short term.
Over the longer term, it's a balance between the gradual loss of angular momentum of the Milky Way as a whole due to drag, gravity waves etc. and the slow growth of the black hole at the centre.
There is an incorrect assumption in this question. There is no "super massive black hole which holds the galaxy together". There is just a super massive black hole.
It is often believed that black holes have a huge gravitational force. Actually, they simply have the gravitational force of their mass. A black hole of 50 solar masses has no more "gravitational power" than a star of 50 solar masses. And if the sun would instantly change into a black hole (of equal mass), the Earth trajectory would not change at all (but yes, you would have to turn on the heater!).
Now, the question is: considering that the black hole at the center of our galaxy is super massive, does it plays an important role for stars like the Sun, at our distance? To answer this, you simply have to ask yourself if the mass of the black hole is important or negligible in front of the mass of the other components that are inside the orbit of our Sun.
The mass of the black hole at the center of our galaxy is about 10^6 (1 million) solar masses (from this paper: http://arxiv.org/abs/0810.4674). The total mass of the Galaxy is about 10^12 (a thousand billion) solar masses (http://arxiv.org/abs/1102.4340). The mass inside the radius of the Sun is way lower (you could calculate it from the speed of the Sun and its distance from the center), but still, the mass of the black hole is very small compared to the rest of the mass inside the Sun's radius. So for the effect of the black hole to become dominant, you would need to be very close from it.
What would happen if instead of this super massive black hole there would be many stars, totalizing the mass of the black hole? Nothing. If would not change anything on the Sun trajectory.
To change the Sun's trajectory and make the Sun "fall", what you would need would be: