Unlike a VCR, DVRs usually have a monthly fee associated with their use. This is because the devices dial into a server once every few days and download new program grids (some DVRs need access to a telephone line, but can be configured to dial in the middle of the night, or at other times when the line is likely to be clear; other DVRs can access program grids through a broadband connection in your home network).
TiVo charges a set monthly fee, though it once offered the option of paying a larger amount once for a "lifetime subscription" (lifetime of the unit, that is). Cable companies that offer DVR packages are usually more expensive than standard cable packages. Some manufacturers offer DVRs that aren't linked to a particular service and don't require ongoing fees at all.
If you don't mind watching your shows on the small screen, an alternate solution exists for PC owners: products like the ATI All-In-Wonder and Sony Giga Pocket cards allow you to capture television signals digitally to your computer's hard drive, in essence using your PC as an elaborate DVR. There is no monthly fee to pay, but you also miss out on some of the advanced features such as constantly updated program grids, Season Passes and the like. Giga Pocket allows you to save recorded programs to VHS or DVD-R, and most video-capture boards have "video out" jacks, making it possible to wire your television to the computer.
ReplayTV, once a direct competitor with TiVo in the standalone DVR box market, now produces DVR software and hardware for PCs. Users must purchase a separate tuner card for their machine. The ReplayTV software provides many of the features found in competing DVR systems.
For lots more information on DVRs, recording devices and related topics, check out the links below.