For many examples of wordhyperbolic groups which I have seen in the context of lowdimensional topology, the ideal boundary is either homeomorphic to a nsphere for some n or a Cantor set. So, I was wondering if this is generally true or there are some examples of hyperbolic groups whose boundaries are neither a sphere of some dimension nor a Cantor set. If there exist such examples, is there any known topological classification of boundaries of hyperbolic groups?

There are plenty of other possibilities. Here are a few examples:
The classification of 1dimensional Polish spaces implies that this is a complete list of boundaries of 2dimensional hyperbolic groups, in the sense that if the boundary is connected with no local cut point (ie the group has no splitting over a virtually cyclic subgroup) then it must be a Sierpinski gasket or Menger sponge (KapovichKleiner). I imagine that a classification in higher dimensions is completely out of reach, though I'm no expert. (Misha Kapovich is active on MO and can provide an authoritative answer.) I'll add full references tomorrow. 

