What is the probability of a standard configuration server failure
because of the failure of hardware in any one year? A standard sort of
server would be something we could buy for about $3000-5000. I would
define a hardware failure as a failure of some physical component of
the server that means the server stops working for more than 1 minute
(e.g. a critical disk drive fails, a physical RAID wipes the disks, a
processor blows up, a bus stops working etc.).

I don't want fantasy figures from server manufacturers but real hard
data from someone who runs a server farm (e.g. RackSpace). I'm happy
with ball-park figures since I'm sure that different configurations
and manufacturers will have differing probabilities.

Really depends on the model.
I've worked in a place where hundreds of servers were bought and
installed for different purposes (thus, different models were bought).
Statistics : 
- 100% failure within 1 year because of a defective fan (a Compaq 1U model)
- ~1% failure within 1 year (another Compaq 1U model)
- 0% (a Compaq 2U model)
- 0% (a DELL 2U model)

Howdy bernardgarbage-ga,

Just a personal point of information on this subject.  I owned/operated an
ISP for 3 years, had around 2 dozen servers, all but one were Intel based
architecture and were half the dollar value of your range, probably because
they were homebrew.

One faiure, in the third year, because of complete hard drive crash, in an
Intel based server.  Cheap, used drive, on a test server, and it had been
backed up, so no real loss.

Looking Forward, denco-ga - Google Answers Researcher