Probably the most famous incident was the Rajiv Gandhi Assasination in 1991 by a woman with explosives on her body. In Sri Lanka, the main guerrila fighers are the LTTE Tamile Tigers. I don't know a lot about them but they've been conducting suicide bombings since 1987.

Large numbers of Japanese civilians committed suicide on Saipan rather than be captured by US forces. I'm pretty sure the same thing happened on Okinawa, too. Large numbers of Japanese civilians were trained as suicide bombers to attack the expected US invasion forces. Fortunately, that war ended before the invasion was necessary.

As for the Islamic woman suicide bomber, who knows what her motivation might've been. One quote from J. Edgar Hoover comes to mind, "Never try to think like a sociopath because then we'd have to worry about you."