Yep, the compressor failing is pretty common, and as mentioned, if the AC is on and the fan is doing nothing then that is the likeliest cause.
I was lucky with mine. When it failed my car was just out of warranty so as a goodwill gesture VW provided the part FOC and contributed 50% of the labour. If your car wasn't bought from a main dealer and/or doesn't have a full VW history then I doubt you'll be as lucky.