Kazuya won the first tournament, got revenge on his father for throwing him off a cliff when he was younger. Heihachi won the second, threw Kazuya into a volcano. Jin won the third tournament, destroyed Orge as revenge for the death of his mother, no one won the third, as the battle was left pretty much undecided.
As for 5, dunno. The tournament itself is for one billion dollars. Check the wiki entries.