It's starting to become well-known that well-published suicides inspire more suicides. There's an explanation on everything2.com, but I'm dissatisfied with the references to heroic portrayal as the explanation for the phenomenon. The Wikipedia entry is much more complete, but it still explains copycat suicides by refering to the media "glorifying the deceased." This "reward" theory is simple--that the media encourages copycat suicides by providing attention and glory as a reward for suicide. The standard sources also explain that media coverage may provoke admiration of the deceased in eulogizing him, and by explaining the causes of the suicide and thus implying that suicide is an understandable or normal response to those causal events.

The reward theory has been debunked somewhat in Cialdini's book Influence,
the Power of Persuasion. Some brief reasons to doubt the reward theory:

• Even consistently negative publicity encourages copycat suicides
• Copycat suicide demographics are surprisingly similar to the original suicide (e.g. 35-year old women don't tend to see Kurt Cobain's suicide as one to copy no matter how much glory is supplied)
• Deaths which are not publicized as suicides but which might have been (car and plane accidents) provoke a rash of similar deaths even though there's no glorifying of suicide.
  

Cialdini's model to explain copycat suicide is more sophisticated than the simple "reward" model -- Cialdini calls the effect "social proof" and it goes beyond just suicide to explain how people copy the actions of those they consider similar enough to be role models. So even if the suicide is criticized unanimously, someone who feels similar (same preference in music, perhaps) will find actions to emulate. In fact, the criticism from the dis-similar people may strengthen the bond felt towards the role model. The bond may be strengthened by the copycat feeling that society is against both himself and the original suicide and provoke feelings of solidarity. Thus, a society that reacts to some unusual person's suicide by criticizing their unusual taste (goth clothes, punk music, or playing dungeons and dragons) may in fact create a self-fulfilling prophecy in calling that taste dangerous and then see a spate of suicides in a population sharing that taste. There's also some evidence (again you can reference Cialdini who discusses Goethe and his hero suicide Werther) that even fictional suicides inspire copycats.

Dorothy Parker seems to have intuitively understood this. I recently read Bobbed Hair and Bathtub Gin, a look at literary culture in the Twenties by examining the lives of Dorothy Parker, Edna St. Vincent Millay, Edna Ferber and Zelda Fitzgerald. Dorothy attempted suicide several times in her life, each time via a different approach, and damaged her own health and reputation. In her short story "Big Blonde", Dorothy wrote:

There was no settled, shocked moment when she first thought of killing herself; it seemed to her as if the idea had always been with her. She pounced upon all the accounts of suicides in the newspapers. There was an epidemic of self-killings -- or maybe it was just that she searched for the stories of them so eagerly that she found many. To read of them roused reassurance in her; she felt a cozy solidarity with the big company of the voluntary dead.

The subtlety of the copycat suicide effect probably means there's no easy solution. It doesn't work to have the media to portray suicides negatively -- that doesn't prevent the social proof phenomenon and may even strengthen it. We probably don't want to instruct the media to entirely suppress news of suicides. Even if we did that, there's still fiction and possibly other art (music lyrics?) -- and even if we censor art there's still deaths-which-might-have-been-suicides.

Despite these subtleties, most journalism codes around discussing suicide in the media focus on the glorification aspect. E.g.

a licensee must not broadcast a program which depicts suicide favourably or as a means of achieving a desired result (ref)

The WHO report from 2000 also talks of glorification and acceptance of suicide as an understandable response, but it goes even further, stating that "certain types of coverage may help to prevent imitation of the suicidal behaviour" (p 6). However, I've not yet seen evidence of that, and I worry that is merely wishful thinking. If Cialdini's model is closer to being correct then the very type of coverage that the WHO report suggests may do more to encourage copycat suicides by mourning the deceased, providing details of their life and families, and providing "risk indicators and warning signs" which can trigger the role model effect.

Update: I've never updated a Wikipedia page before, but this seemed a good time to try. I added the paragraph on Cialdini's social proof model.