Suggestions for multilevel backup of single machine?

[James Youngman <jay@gnu.org>]

Here's my current backup arrangement:

Data is stored in filesystems on LVM volumes over RAID1.  While RAID1
presents some protection from disk failure, it gives no protection
against data corruption due to flaky hardware or data loss caused by
fire or theft.

Therefore I have an offsite backup arrangement.   This consists of two
rsync backups.  One backup goes to a local disk (different disk
manufacturer, different disk controller) and the other rsync backup is
to a disk at work.  This works a bit but the outgoing bandwidth on my
cable connection is low (about 0.3 Mbps).  If I make a large change to
the machine (e.g. dist-upgrade) I physically swap the home and work
backup disks (this is the main reason for keeping the local backup
too).  This at least allows me to place an upper limit on the amount
of data I would lose in the case of (e.g.) a fire.

However, there are two respects in which I think some improvement
would be useful:

(1) Quite a lot of the files on my system are files I never expect to
change again.  I plan to write a few scripts which will tell me if a
file that hadn't been modified in, say, two years was in fact recently
modified.  This could give me early warning that the disk controller
has gone berserk (again).

(2) It would be useful to have a historic backup capability too (e.g.
the way the filesystem looked yesterday, last week, last month and a
year ago), at least for filesystems like /home.

What are good solutions for doing (2)?   (Please only recommend
software you're using yourself :)

Thanks,
James.