Beware, if you copy files, 'en mass' you also risk copying any virus file, spyware etc at the same time, especially if you try and copy program directories. It's much better to transfer only the specific data files you need.
In terms of speed, putting the HD into the new machine is certainly the quickest way to transfer the data. then networking, as mentioned above, in that only one operation is requried as such, copying to a removable HD is a valid method (especially over USB 2.0), but will be more tedious, and much slower if the original PC only has USB 1.0.