It definitely varies by hospital.  We went to a ultra-modern Chicago downtown hospital, and didn't receive any sort of video recording (nor did we have the option of such).  What we received was printouts on tape (very high resolution version of cash register tape, the kind that is printed on with heat imagery).  Black and white pictures (which is consistent with a regular ultrasound), nice looking, but not video.  10cm square sounds about right.  

We did two ultrasounds (as do most people nowadays), one at 12 weeks to confirm it wasn't ectopic, and one at 20 weeks for various diagnostic purposes.  We got some pictures during both appointments.  During the second one they take quite a few pictures, and if you have a friendly tech you should get several good looking pictures there (including the 'boy or girl' picture at that appointment).