The answer is broad, to give you an idea, after soul is left the body, according to the sect which one belongs to, there is tradition to decompose/destruct the body. Here are few exmaples for it..
If a baby dies, body would be buried in the earth and not cremated.
I heard from someone that if a saint/sanyasi leaves his body, his body would be cut into four pieces and spread the pieces across four sides of forest in order to feed animals(may be considered as he lived for others and even after he leaves this world he is helpful to someother being in this way). There are also instances where they disappear/leave their body in a sea. If not it would be buried in a place and the place is worshiped as brindavan
In general the resistance power of the aged or diseased will be low and would be adobe of many harmful microbes, so it is cremated
The most important cause is after the body is cremated, ash will be collected from important body parts and is dissolved into holy river water, it is believed that this will free the dead person from hell and may give better life next time. (so is organ donation is not well popular)