"Suicide bombing" is not simply direct suicide. None of the answers here actually address "suicide bombing"; they only address suicide. It is simply a term used by those who disagree with it. A suicide bomber will refer to themselves as a "martyr" - someone who faces certain death to defend Islam.
Faced with a different audience and different situations, I think you'll find very different answers to this one. It's remarkably easy for someone who lives in a modern society to consider suicide bombing as unnecessary, but there are situations where it is indeed defense.
There are many of the Prophet's Companions who went to war with near suicidal odds. But it's not the same analogy as suicide bombing, because a suicide bomber has a 100% chance of death.
There are no weapons during the early Islamic times which could deal the kind of damage suicide bombs do, with the same degree of certain death.
The closest I can find is a situation in the Ridda wars, in the battle against Musaylimah:
o Muslim army: 11000, Musaylimah's army: lowest estimate was 40000
o Musaylimah's army backed into a garden and sealed it. The garden became known in history as the Garden of Death because of the many people killed there on that day.
o One Muslim soldier asked to be thrown into the garden so that he could open the door from the inside. Who was this very courageous soldier?
This man was al-Baraa ibn Malik al- Ansari, the brother of Anas ibn Malik, the personal aide of the Prophet. He was thin and wiry with so little flesh on his bones that it was painful to look at him. Yet in single- handed combat he defeated and killed many opponents and in the thick of battle he was an outstanding fighter against the mushrikeen. During the battle against Musaylimah, al-Baraa went forward and addressed his company, "Put me on a shield. Raise the shield on spears and hurl me into the garden near the gate. Either I shall die a martyr or I shall open the gate for you." He sustained numerous wounds before he could open the gate. (taken from "Companions of The Prophet", Vol.1, By: Abdul Wahid Hamid) (Source)
(Also another reference to the same story in Huroob Ar-Riddah, by Shauqee Abu Khaleel, pg 92)
The situation was of someone who, alone, faced near certain death to hasten a siege. He survived, but jumping alone into a room filled with enemy soldier is near certain death! This was also an offensive maneuver, not one done by someone who is backed into a corner.
There have also been plenty of other near-suicidal moves done by the Sword of Islam, Khalid al-Walid himself. As these were some of the Prophet's companions, it could be argued that it is an Islamic approach to sacrifice oneself for the greater good.
Again, this is a poor analogy, because there were no suicide bombs during the Prophet's time.
It depends on intention and situation. If a person is going to blow up civilians out of spite and desperation, of course, it's haraam. If a person does so to enable a decisive victory in the name of Islam, history seems to encourage it.