When is it appropriate to use
rsync for backups?
Having expended far too much time with dump, it is probably best relegated to history. Its primary design goal was to be as efficient as possible with slow filesystems and the constraints of magnetic tape.
Those design criteria no longer obtain and I cannot imagine a situation (aside from legacy systems) where dump would provide any advantage.
dump is traditionally used in cases where you need to image an entire device once, and not keep backing it up incrementally. Since it was created in a time where magnetic tapes were popular, random disk writes were not all that possible, making incremental backups nearly impossible.
rsync is a more robust tool that doesn't try to account for those obsolete technologies. This allows it to have random access to the backup destination and lets it take true incremental backups.
dump functions at a lower level than rsync, so you can actually ask it to dump unmounted filesystems, which AFAIK isn't a possibility with rsync. Other than that, rsync is a superior tool in almost every way, and allows you to minimize transfer, which is especially useful over network backups.
In addition to the other answers, rsync's ability to run on most operating systems (even telephones!) and it's sheer ubiquity and popularity make it my choice.
rsync is not a backup tool -- it is a copy tool. If you want to use a simple copy as a backup method, then
rsync is a good tool to accomplish that.
dump gets you an archive file that can be compressed, so it takes up less space than a simple copy, and can be split across multiple backup disks and put on write once media. It also can do incremental backups both for speed of daily backups, and so you have multiple snapshots in time you can go back through looking for a specific version of a file. You can get something similar with
rsnapshot which uses
rsync and hard links, but it requires the backup medium to be a single hard disk that is large enough.