Just wanna add some thoughts about Nelson:
It's my understanding that he as admiral surrounded himself with very capable captains, who understood all the elements in his overall stategies and knew exactly what they had to do and when. That's an incredible important factor (often overlooked) - the ability to pick out the commanders you know can make a difference in battle.
At Copenhagen, his bold manouvre secured him most of the Danish fleet (which was quite considerable at that time) as a prize. The bombardment of Copenhagen (civilian casualties) amongst other things aren't that pretty to look back upon, but from a military standpoint you got to admire his boldness.
His victory at the Nile, sealed Napoleans forces in Africa and gave Boney a lot of trouble. It had a huge significance of the European landscape.
Trafalgar - well, after that England ruled the seas for a century afterwards. The trade income from overseas made England wealthy beyond imagination.
As someone else mentioned, luck in itself is not enough - you need to know how to make the most of the luck you are given. Your ablilities will have to do the rest.
He is probably one of the greatest naval commanders of all time.
As a sidenote - everybody interested in naval warfare who gets the chance to visit the UK, should visit Portsmouth and check out The HMS Victory. I did with my parents when I was like 16-17 years old and I will never forget that experience.
Mediocre generals - well, perhaps some of the commanders of The Vietnam War, Afganistan War (Soviets) and the first Gulf War...