I am afraid I am not an expert on the time period in question, but I can say with confidence that taking the heads of prominent samurai, generals, and warlords was an established practice during battles in the Sengoku Period. It was done both for the perceived honor of the achievement and the expectation of a reward.

If a very famous samurai were to fall form his horse during a battle, it was very likely that the common spearmen (ashigaru) would scramble to be the first person to claim his head. I am not aware of the specifics of how the reward system worked, but I have read about money, land or increased social standing as possibilities. I would guess the rewards would be up to the whim of the common soldiers' superiors.

(As an interesting aside: When warlord Takeda Shingen's brother Takeda Nobushige was killed in battle at Kawanakajima, an enemy spearman beheaded his corpse. However, a Takeda samurai killed the spearman and recovered Nobushige's head. I am not sure if the samurai was rewarded for recovering the head, but Takeda Shingen was said to be grateful for the opportunity to bury his brother's severed head and body together in a single grave.)