1. In this post I'm speaking about karate katas since that's what I am most familiar with. Those of you in different disciplines please feel free to comment on your style.
2. Most people that I have encountered tend to argue the relation between kata and kumite as far as sport karate fighting (point fighting, full-contact or kickboxing for example) is concerned. The one thing to remember is that these kata were made LONG before there was a such thing as sport karate.
3. Katas were made for self-defense purposes, namely to defend one's life in a life-or-death scenario.
4. To help spread karate to the masses (especially children) many of the more lethal techniques were substituted or "covered up."
As you may have guessed, the correlation I'm speaking of is kata to kumite as far as actual street fighting/self-defense is concerned. Granted there may be some correlation to sport karate (correct technique, focus and timing immediately come to mind), this is not what the katas were originally intended for. They were intended to show the best basic techniques designed to defend one's self and to end such a confrontation quickly and decisively.