All analog TV tuners, be them in televisions, VCRs, DVRs, or computers, will cease to function for broadcast stations unless a digital converted box is inserted in between. However, this switch over only affects over-the-air channels you'd pick up with an antenna, not cable or satellite TV services. It's up to the individual cable/satellite companies when they want to make the switch, and what options they will make available. So far I have not heard of Comcast, Time Warner, and the rest setting any definitive timelines so you should be fine for the near future.

Hope this helps,
John