Has anyone ever experienced lost or corrupted files due to defragmenting drive volumes? Is this safe to do with projects, video, audio or any critical files still on the disk(s)?

Has anyone ever experienced lost or corrupted files due to degragmenting drive volumes?
No.

Is this safe to do with projects, video, audio or any critical files still on the disk(s)?
For practical usage, I would say yes.
Defragmentation does not create any more risk than normal. It will likely save you as it goes a long way towards preventing dropped frames. However, do not defragment excessively as it is pointless and creates excessive usage on your drives.

To keep fragmentation down, create a partition just for large files (i.e. video files). Do not installs programs onto that partition. If you have seperate drives, you don't need to create seperate partitions except for the system drive (if you want to use that for video).

If your data is important, keep backups. With most editing programs, you can backup the project file and non-video files (i.e. titles, graphics, CG, music) and with that project file you can re-create your entire project. The program can re-capture your original footage off mini-DV tapes.

Solid advice from Glen.

I'll just add that if one ignores defragmenting, it will eventually lead to performance problems. The more the hard disk's heads have to dance around to find clusters of data, the slower the throughput. Seen it many times.

Also, don't let a hard disk get within a few GB of being full, especially a "C" Drive.