That is an answer that could get someone killed - yes, killed. I have been working with CRTs for over 50 years (we used to call them picture tubes). When a CRT implodes shards of glass can fly over 30 feet. I have seen it. Others in the room could be injured as well. The ultor (second anode) voltage is nothing to sneeze at either. And yes, I have gotten shocks from 277 volts (one leg of 480 3-phase to ground) no fewer than three times. Your first could be your last. Understand that. Respect that. That will leave you sore for a week if it doesn’t kill you. Virtually every day I work with machines that need lethal voltages to do their jobs properly. I am not afraid of them but I am always respectful of the injury or death they are capable of. But you needn’t be afraid of a CRT monitor - or an old school TV set either. Be respectful of the voltages it carries and the fact that any high voltage item - even if it is only a few milliamps - can injure you. I changed my first picture tube (a 19” black and white)...
Grounding it to a wall outlet does nothing; there is a grayish-black coating on the outside bell of the CRT (called Aquadag) and you will notice some type of metal spring or finger touching it - THIS is what you want to ground the wire to. But even more important the CRT is made of glass and it contains an extremely high vacuum. If it breaks it will implode and glass will go flying everywhere. I strongly recommend at least wearing safety glasses before handling it. Update (11/28/2011): I have been working with CRTs since I was about 10 years old (1970) and the points raised are all very valid. I illustrate the fact that it can be worked on safely - even by a kid - but if you read this and do not feel comfortable with this, please, don't touch it and leave it to qualified personel. The second anode connection on the side of the bell is the high voltage connection. In ALL cases make sure it is not plugged in! After carefully removing the cover, you should be aware of exactly what you are trying to discharge....
Good answers; in wet or humid areas many times florescent fixtures are enclosed. Also, your bulbs may be dirty - when moistened by humidity it can form a short circuit around the bulb and keep it from striking (starting).