"Basic" cable is almost certainly analog - at the moment. If you can receive the channels on a standard TV plugged into the wall and no converter box, and you didn't have the TV scan for digital channels (for a new TV with a digital tuner), then it is certainly analog. So you can use an analog tuner card like the Hauppauge 1600. This card also has a digital tuner that can receive over the air ATSC digital broadcasts with an antenna. It also has a digital QAM tuner for unencrypted digital cable. However, there are probably few to no unencrypted digital cable channels. This varies by cable system (I have none, others report that Comcast carries the local channels in unencrypted digital).
The long term availability of analog cable is up to the cable companies, as I understand it. Once essentially all TVs have digital capability (after the end of analog full-power broadcasts in Feb. 2009), I believe they will be free to end analog cable. I would expect them to encrypt everything and require us to have a STB.
Long story short, most people recommend the Haup 1600 for US viewers.
I don't think the HVR-950 will work for analog since it does not appear to have a hardware encoder for the analog input. It should work for OTA ATSC. The HVR-1950 has the hardware encoder that you need for GBPVR with an analog input.