Kamikaze is a word in the Japanese language that translates as "Divine Wind." It originally referred to severe storms that wrecked two separate 13th century attempts to invade the Japanese islands by the Mongols under Kublai Khan. The term was later used to describe a type of military tactic in which a pilot of a vessel deliberately rams another vessel, killing themselves in the process, as well as severely damaging or destroying the other vessel.
The latter usage of "kamikaze" originated on Earth during the Second World War. Seeking to stop the advance of American forces, Japanese forces often made such suicide runs against Allied ships, often in planes laden with explosives. The term was an allusion to recruit these pilots: it was hoped they would prevent the invasion of Japan by a foreign fleet as the storms did centuries earlier. A number of American vessels were either destroyed or disabled in the process. While the use of Kamikaze tactics did some damage to the American fleet, it did little to slow the advance of American forces as they drove the Japanese forces back to Japan. (Historical accounts)
After being taken over by the Ravens, the Frenni merchant vessel Selessan tried to trick the crew of the USS Enterprise into sending a landing party to their ship as a first step towards taking control of the Enterprise. When the Enterprise scanners showed that there was no Frenni or Klingons on the Selessan, Kirk confronted the Raven who had taken the Captain's brain. The Ravens realized that their plan to take over the Enterprise had failed, and made a Kamikaze run on the Enterprise. While the Enterprise was able to raise her shields prior to impact, she was still seriously damaged - with one pylon damaged beyond repair. (TOS novel: Dreams of the Raven)
During the first Borg invasion of Sector 001, there came a point where the USS Enterprise-D faced almost certain defeat. Realizing this, Captain Riker ordered Ensign Crusher to set a collision course with the Borg Cube, and ordered Lieutenant Commander La Forge to prepare to engage the warp drive. It is not known if such a Kamikaze maneuver would've destroyed or disabled the Borg ship - before Riker could order Crusher to engage Data called and reported that he was going to try to access the Borg regeneration routine. That attempt worked, and the Borg shut down for their regeneration cycle. Then a few moments later a malfunction destroyed the Borg ship. (TNG episode: The Best of Both Worlds, Part II)
Due to a chemical imbalance brought on by a lack of certain elements from their systems, the members of the Jarada hive Zel began to go insane. A number of Jaradan pilots engaged in Kamikaze attacks against the Enterprise. As the shields were up, the USS Enterprise-D suffered no permanent damage. While some of the pilots were beamed off their ships at the last moment, a number of other pilots could not be saved, and died when their ships crashed into the Enterprise shields. (TNG novel: Imbalance').
The Jem'Hadar have also been known to engage in Kamikaze like tactics. In 2370 a Jem'Hadar vessel rammed the USS Odyssey, destroying both ships in the process, and pointing out to Starfleet just how far they would go to serve the Dominion. (DS9 episode: The Jem'Hadar).
In an alternate timeline, Captain Kathryn Janeway once used a Kamikaze maneuver against the Krenim temporal weapon ship. Her ship had already been heavily damaged by the Krenim, and during an attack on the temporal weapon ship Voyager was damaged even further, especially when another ship collided with her. With weapons and most other systems off line, Janeway set a collision course with the ship. Voyager was destroyed when it rammed the Krenim ship, and the Krenim ship was destroyed a few seconds later. When the Krenim temporal weapon was destroyed, history was reset to its original state, and this timeline was erased. (VOY episode: Year of Hell, Part II)