FWIW, I've personally never heard a corroborated story of someone dying from anything of an electrical nature inside a CRT monitor. While the HV can certainly give you quite a jolt, the nature of it is such that, if the monitor's off, it's not overly likely to kill you (but discharge the smurfing thing before taking off the anode cap!). I'm sure it's happened, but I've not heard a story with any evidence. I would suspect that you have as much chance of dying from physical injury resulting from sudden, forced or reflexive movement as from the electrical jolt itself (due to heart issues, most likely).
Now, if you're working on something while it's on, watch out for any unisolated area of power as rickn says. While the HV is a concern, it'll stay put underneath that cap unless you go messing with it. Of more concern is the power input section (or the whole board if it's unisolated in any way). While I've never heard of anyone dying from anything electrical in a CRT monitor, it is well known that "the wall" can cause death, and that's basically what's present inside that monitor in some places.
I have, however, heard stories involving some degree of corroboration where someone suffers serious injury or death due to the vacuum of the CRT (including a particularly gruesome one where somebody managed to stab themselves in the gut with the neck of the tube by carrying it the wrong way). There's a lot of potential energy in the vacuum relative to atmosphere. Don't do anything to compromise it.