Do you know of any tried and tested incremental/differential backup software system, to backup only newly added or modified HDD data to DVDs?
And preferably software which can easily restore all of these fragmented backups when needed.
Acronis True Image Home does everything you would want/need in a backup software.
I've been using Genie Backup Manager Home for about two and a half years. It will backup to DVD (among other targets), and restoring from fragmented backups isn't a problem (I've done it.) I have it scheduled to backup any changed files to DVD-RW every night. They also have a Pro version, and a new product that backs up as you work (Timeline).
SyncBack from BrightSparks can incrementally backup data to CD/DVD.
It has a neatly designed interface with a wizard to configure a backup profile initially. After this you can modify "easy" and "expert" profile settings in a categorised window. The help files are linked to the interface, so clicking Help on any screen shows you context-sensitive info.
It has some nice extra features though I've not worked with these myself.
Not exactly a backup software, but git can do all of that.
Although it's now a version control system, it actually started as just a bunch of 'file-system' utilities that would provide a basis for a version control system to be built on top of it.
It can be used to make incremental backups and the data can synchronized over many places. (Though not ROM mediums)
It's highly reliable, too.
ShadowProtect is extremely fast and allows you to do HIR (Hardware Independent Recovery).
Compared to Acronis or Norton Ghost it is very fast and runs very well.
You can create partitions while restoring the backup and optionally set the MBR to be recovered.
I switched from Acronis since Acronis isn't as good now as it was with version 7/8 (Too slow now).