This is most definitely possible but it also depends on what type of DVR you're referring to. Dish PVRs and ReplayTVs require that you pull the drive and place it in your PC for extraction of the mpeg files using a PC-based utility. Tivos can be connected to your PC via a home network and extracted remotely, but only after the Tivo has been "hacked" (i.e., the OS must be upgraded and some other software manipulation must be performed on the Tivo itself to enable network functionality for extraction). The format of the mpeg files is basically a variation of mpeg2 and differ from each other slightly. As such there are various utilities that are required to process the extracted mpegs in order for them to be authored to DVD.
There are forums dedicated to the different types of DVRs and the methods used. Unfortunately, discussion of this topic is somewhat verboten at the Tivo Community Forum which is run by the mods here at the AVS Forums. I'd post links to the other forums but they censor any such info when it's posted.
Hard drive upgrades are relatively easy on Tivos and ReplayTVs. Dish PVRs are a little more complex and require a bit of hacking knowledge that goes beyond the legal limits of these forums. For Tivos, check out Hinsdale's How To which is basically the de facto reference for upgrading or replacing a Tivo hard drive.http://www.newreleasesvideo.com/hinsdale-how-to/
The process does not require a Linux machine as Axatax suggested but rather a Linux boot disc that is used in a Windows PC. MFS Tools 2.0 is the latest boot disc containing the necessary utilities. If you plan on upgrading to a drive larger than 137GB you'll need the version with large disc support. Both versions are linked for download from the above site.
For ReplayTV drive upgrades, check out the ReplayTV Project site at sourceforge.net:http://rtvpatch.sourceforge.net/
If you've got a proprietary DVR from Comcast, Time Warner, or some other variety you'll have to do some google searches to see if there is any info available for these models as I am not familiar with them. If you've got an UltimateTV DVR then search through the UTV forum here at AVS for info on upgrading the hard drive. UTVs can only be upgraded with specific model hard drives but they are the easiest units to upgrade since all you have to do is swap out the drive and plug everything back in. The software gets downloaded automatically when the new drive is detected.