I really doubt disk copiers like CopyWrite or the such would work on XP. Too much low-level disk routines. For not-protected disks I used pkzip keeping in mind to store hidden files and the label. One volume per disk.

Unix people can use this:

1dd if=/dev/fd0 of=diskimage

Reads the whole floppy sector-wise and copies it into a file called "diskimage". The file can be written back to a disk by reversing the arguments for the if and of parameters. Depending on the kernel configuration the image can also be mounted directly.

On the Windows platform I've tried WinImage once. It's shareware and has some nice features.

These two solutions will not cope with the more sophisticated copy protection mechanisms like weird sector sizes or some of the PC booter protections, but they should be useable with at least 90% of all games released on floppy disks.

The best backup utility out there is FIRM ( Floppy Image Reader/Maker). It can read and write disk image's and is a great program that is only 12kb.

Works in XP but must be ran through the command prompt.

http://sac-ftp.externet.hu/utildisk8.html

I also used pkzip for most of my dos game collection. I had very few that had on disk copy protection since I didn't start dos gaming until 91 or so. By then they had moved more to look up the word in the manual on page 3 paragraph 2 line 7 method of protection rather than physical protection. I can only rember Lemmings actually having disk protection. Many of my Amiga disks were protected with bad sectors or the like, but not my PC ones.

As el_Pusher said if you use pkzip be sure to include hidden files and volume labels. Several programs checked the volume label during install, Access Softwares Links Course disks come to mind, as well as GEM and a few others that wouldn't install without the correct volume name.
-$ for volume labels
-jhsr for hidden/system/read-only files
I still remember those switches after all these years

Well there's also programs like Neverlock to help you out there.