How do I combine/join/merge all vertices at the same location? So I imported this *.obj model file. It is a mesh that has all the faces exploded/split/whatever, meaning that the thing is a collection of separate polygons that are not connected to each other. There's hundreds of them. So I selected all the vertices with A and tried to merge them with Alt+M, which of course deleted the whole model, because it merged all the vertices into one. So at the location of each polygon corner can be up to six vertices, each belonging to a different face that are directly adjacent to each other, yet not connected to each other. Is there some sort of a smart functionality in Blender that recognizes duplicate (or more) vertices at same location and merges them?

I am quite a n00b at this, so please forgive me for not having the best grasp on the correct terminology.
You are looking for remove doubles. It can be found in the 3D view tool shelf while in edit mode.