Suicide bombers conducted 658 attacks around the world last year, including 542 in U.S.-occupied Afghanistan and Iraq. . . more than double the number in any of the past 25 years. . . More than four-fifths of the suicide bombings over that period have occurred in the past seven years, the data show. The bombings have spread to dozens of countries on five continents, killed more than 21,350 people and injured about 50,000 since 1983, when a landmark attack blew up the U.S. Embassy in Beirut. . . . since 1983, bombers in more than 50 groups from Argentina to Algeria, Croatia to China, and India to Indonesia [have used suicide bombers]. . . . Of 1,840 incidents in the past 25 years, more than 86 percent have occurred since 2001, and the highest annual numbers have occurred in the past four years. . . . The data show more than 920 suicide bombings in Iraq and more than 260 in Afghanistan, including some that killed scores of U.S. troops. All occurred after the U.S. invasions of Afghanistan in 2001 and Iraq in 2003. . . . At least two-thirds of suicide bombings since 1983 have targeted U.S. policy goals[.]
From the Washington Post.
Prior to Iraq and Afghanistan, suicide bombings were often associted with the Tamil Tigers in Sri Lanki and with the Israeli-Palestinian conflict.
The Liberation Tigers of Tamil Eelam, popularly known as the Tamil Tigers, is an avowedly secular rebel movement of the country's Tamil ethnic minority. It carried out scores of suicide bombings from the late 1980s until a cease-fire in 2002. The conflict between the Tigers and the government, which is dominated by members of the Sinhalese majority, began in 1983 and claimed an estimated 65,000 lives.
Though dominated by Hindus, the Tigers are predominantly ethnic and nationalist in outlook, with religion not playing a significant role in their actions. . . . The rebels carried out their first suicide bombing in 1987, when a captain blew himself up along with 40 government troops at an army camp in the northern part of the country. . . . [T]he group accounted for 76 of 315 suicide attacks carried out around the world from 1980 through 2003, compared with 54 for the Islamic Resistance Movement, or Hamas, and 27 for Islamic Jihad. . . .
Even as the Tigers have abandoned suicide attacks, others have adopted the tactic as their own. In Russia, Chechen Muslim radicals have mounted at least 19 suicide operations . . . including those in one terribly deadly week last year when hundreds died in a fiery siege at a school, a bombing at a Moscow train station and the downing of two airliners.
Al Qaeda has also favored suicide plots on more than 20 occasions since 1996 against the United States and its allies, including the unprecedented Sept. 11, 2001, hijackings that killed nearly 3,000 people. . . .
[Ed.A source different from the one in the first blockquote in this post estimates that] 31 of 35 groups that have used suicide bombings are Islamic. . . .
Judging by statistics, Israeli officials have made significant progress against suicide attacks since the start of the intifada in September 2000. At the height of the uprising in 2002, 42 suicide bombings killed 228 people. Two years later, the number had dropped to 12 bombings and 55 deaths.
Israeli officials say the construction of a concrete barrier that rises 24 feet high in some places and the intensive military operations in the West Bank have helped keep suicide bombers out of Israel. In addition, the Israeli military destroys the family homes of suicide bombers, a practice human rights groups have condemned as an illegal exercise of collective punishment.
Also from the Washington Post.
A summary of a report on the demographics of suicide bombers in the Israeli-Palestinian conflict can be found here
Approximately 90% of suicide bombings in Iraq are conducted by foreign fighters. "According to the U.S, military, records seized from al-Qaeda show that 40% come from North African countries such as Libya and Algeria, and 41% from Saudi Arabia." But foreign fighters are believed to make up a very small proportion (less than 1% of individuals detained by U.S. forces) of insurgents in Iraq.
Suicide bombings in Afghanistan began in notable numbers in 2005 and picked up dramatically in 2006 and 2007, although the Afghan attacks have often tended to inflict fewer casualties than those in other areas.