Most manufacturers will quote an MTBF (Mean Time Before Failure) of
somewhere in the 30,000 to 60,000 hour range, EXCLUSIVE OF the CRT. The
typical CRT, without an extended-life cathode, is usually good for
10,000 to 15,000 hours before it reaches half of its initial brightness.
Note that, if you leave your monitor on all the time, a year is just about
8,000 hours.
The popular rationalization for what is most often just laziness is that
power-on is a stressful time for any electronic device and reducing the
number of power cycles will prolong the life of the monitor. With a properly
designed monitor, this is rarely an issue. Can you recall the last time
a monitor blew up when it was turned on? The other argument, which has more
basis in reality is that the thermal cycling resulting from turning a monitor
on and off will shorten its life. It is true that such thermal stress can
contribute to various kinds of failures due to bad solder connections.
However, these can be easily repaired and do not effect the monitor's
heart - the CRT.