Well, DVRs cover a pretty broad spectrum of devices, including PCs that have had DVR capability added with a tuner card.
DVRs from the cable company have full access to everything your cable account has access to, at full quality. However, as mentioned before - many of these will refuse to even boot if they don't have a connection to the cable network. They implement Digital Rights Management (DRM - sometimes called Digital Restrictions Management, which is a more appropriate name) to make sure it is not possible to copy the contents to a hard drive or other machine.
Standalone DVRs (such as TiVo) tend to be more flexible in terms of operating without input, but still apply DRM to most recordings. Sometimes they are not able to access all content available on your cable network. Some of these MIGHT allow archiving of some content to DVD or an external hard drive for playback on another device, but most likely - you'd have to haul the whole box with you.
PC-based DVRs tend to be the most flexible, but also the hardest to use. These rely on adding a TV tuner to a PC.
Windows Media Center Edition can, in some cases, access encrypted cable content. However, as I understand it, this can only be done if you purchase the DVR solution with the PC itself. Blame CableLabs' insane restrictions for this.
Other packages like SageTV can only access the following:
Unencrypted digital signals (OTA broadcast TV via antenna, or unencrypted cable, which is usually limited to the major broadcast networks) - This is the digital component of Hauppauge's WinTV-HVR devices
Recordings of the analog output of a cable or satellite box using a video capture/compression device (Such as the analog portions of Hauppauge's WinTV-HVR devices). This usually limits quality to standard definition, the only exception I know of is the Hauppauge HD-PVR 1212 which can record component video signals in high definition.
Often packages like SageTV do not apply DRM to their recordings, allowing you to copy them to an external hard drive or another PC, so for example you could watch recordings on a laptop.
In my case, I have an old Hauppauge WinTV-PVR 500 for analog recordings off of my cable box, and a SiliconDust HDHomeRun for digital recordings of network TV off of my cable system.
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*disclaimer* I am not now, nor have I ever been, an employee of Best Buy, Geek Squad, nor of any of their affiliate, parent, or subsidiary companies.
