While in college, I was taught that the practice of kamikaze only existed for Japanese pilots who realized their aircraft was going down. If a pilot realized they were going to go down, they would aim their aircraft at a ship instead of hitting the open water. This makes sense considering that since steel was limited and wasting a perfectly good plane seems irrational and counterproductive.
However, I've read a couple of pieces talking about dedicated kamikaze units which had explosives loaded into the planes. This seems to indicate a determination to kamikaze rather than a secondary option.
Basically, of the 3,860 kamikaze pilots that were killed, (a) how many of them had pre-loaded explosives in them and (b) how many of them were of the "I might as well hit something" variety
I don't have much in specific numbers, maybe someone else can provide some, but here's something that may help.
"The Battle for Leyte Gulf marked the first appearance of kamikaze, or suicide, planes. On October 19 (1944), Vice-Admiral Takijiro Ohnishi had met with senior commanders at Mabalacat fighter base in the Philippines and announced: 'With so few planes we can assure success only through suicide attack. Each fighter must be armed with a 550-pound bomb and creash land on a carrier deck.' "
-The American Heritage Picture History of World War II, by C.L. Sulzberger, page 532.
I'm somewhat of a WWII history buff, but I've never heard of the practice of crashing planes into ships as a last resort; I've always heard that they took off knowing that they'd crash into ships.
I think in the beginning of the war the pilot's code of honour would have demanded that they tried to take as many of the enemy with them as possible if they were hit or wouldn't make it back, but considering the way planes behave once they're badly shot up (on fire, loss of control surfaces, control cables, inability of the pilot to control the aircraft) then I think it wouldn't have been that easy on a lot of occasions to aim at a ship, let alone keep the plane on course to hit it.
Later on in the war, once the Japanese realised it wasn't going their way, there was a definite shift towards kamikaze units - they were running out of experienced pilots, and they were short of aircraft and the resources to make more.
Towards the end of the war, as /u/ezcompany210 said, they did start to give their pilots bombs and say "fly into a ship" but they also started developing kamikaze aircraft called "Cherry Blossoms", made out of as little material as possible. They were launched from bombers, but the bombers were so vulnerable to attack from the Americans that most of them were lost either in accidents or before they had been launched.
