Are we moving ever closer to the center of our Galaxy due to a super massive black hole? 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.