A single stage rocket is desirable from a technological point of view since it sheds a lot of complexity: you don't have to deal with multiple engines, separation mechanisms, structural considerations, etc. However, multi-stage rockets can deliver more real payload to orbit, since they maximize the amount of fuel that is spent on taking the actual payload up there.
Single-stage rockets need to carry a lot of dead mass (empty tanks and engines) all the time, and that is a lot of wasted fuel. A multi-stage rocket can dispose the big first stage engines once it's cleared out most of the Earth's gravitational pull and use smaller engines to continue.
Another important consideration is that rocket engines don't run optimally during the whole burn. The first stages are optimized for atmospheric conditions, whereas later stages are optimized for vacuum conditions. Therefore having one big engine propel you up all the way incurs in an even grater loss of fuel due to the inefficiency at high altitudes. You could probably have a rocket engine capable of having a variable geometry to compensate for this but AFAIK is almost impossible to do it.
See the following for more details:
[1] http://en.wikipedia.org/wiki/Staging_(rocketry)#Advantages
[2] http://en.wikipedia.org/wiki/Rocket_engine_nozzle