The World Health Organization estimates that in the year 2000 approximately one million people will die from suicide. A global mortality rate of 16 per 100,000. One death every 40 seconds.

The WHO further reports that:

In the last 45 years suicide rates have increased by 60% worldwide. Suicide
  is now among the three leading causes of death among those aged 15-44
  (both sexes). Suicide attempts are up to 20 times more frequent than
  completed suicides
Although suicide rates have traditionally been highest among elderly males,
  rates among young people have been increasing to such an extent that they
  are now the group at highest risk in a third of all countries
Mental disorders (particularly depression and substance abuse) are
  associated with more than 90% of all cases of suicide. However, suicide
  results from many complex sociocultural factors and is more likely to occur
  during periods of socioeconomic, family and individual crisis (e.g. loss of a
  loved one, employment, honour)
   

In the US, the Centers for Disease Control reports that:

More people die from suicide than from homicide. In 1997, there were 1.5
  as many suicides as homicides
Overall, suicide is the eighth leading cause of death for all Americans, and is
  the third leading cause of death for young people aged 15-24
Males are four times more likely to die from suicide than are females.
  However, females are more likely to attempt suicide than are males.

Statistics about suicide are difficult to collate, and may be inaccurate because of the sensitivity of the issue, particularly in countries where suicide is an absolute taboo. You can find suicide statistics in the following English language sites:

International Statistics: World Health Organization - for international suicide
  statistics, including the most recent global stats by country
USA Statistics: American Association of Suicidology - for USA suicide
  statistics
New Zealand Statistics: New Zealand Health Information Service - for NZ
  Statistics. There is also specific information about NZ youth suicide
Canada Statistics: Canada Statistics Agency - for Canadian suicide
  statistics
UK Statistics: UK Samaritans provide statistics for the United Kingdom
  and the Republic of Ireland

Statistics for further countries will be added as they become available to us in English or translation from trusted sources.