Im going to clarify my top 5 as well.
Woody Allen - A bit like what Bilbo said, the enthusiasm of my mother for Woody rubbed off on me when I was growing up. One of the wittiest men of his generation, in my opinion. The man's life is a train wreck but he exploits that to the full benefit of his art, while all the time denying his films have any element of autobiography in them. As with most of my favourite film makers, one of the things I like best about Woody is his work is so original. I guess the downside of that is it is not everyone's taste but for those who get his humour the man is a genius.
Francis Ford Coppola - When I did my top 10 films of all time I did not put Apocalypse Now in there, which in retrospect was probably wrong. The Godfather trilogy is also awesome (the third one is actually not a bad film, but suffers from its association with two unparalleled works of art.) I love the fact the man has made films for the mainstream but is happy to make a film without mass appeal, like The Conversation, purely because it fulfils his sense of being an artist. I also love the lengths he is willing to go to to get his films right - the man is a perfectionist, and it shows in his work.
Martin Scorsese - In a way I have least to say about Scorsese. Putting him in because of the consistency and brilliance of his films: Goodfellas, Cape Fear, Mean Streets, Gangs of New York. A little more consistently mainstream than Coppola but happy to lead rather than follow. I love the depth of the characters in his films which allow you to be immersed in the story.
Takashi Miike - This director makes you ask what makes you watch films in the first place, what you look for in a film. I have to be honest, depending on your definition of "enjoy", sometimes I don’t enjoy his films. They are often an ordeal. There is a time and a place for a film that you sit and enjoy but ultimately know inside out, even before you have watched it - such is widespread adherence to the Hollywood formula. Films can be touching and sentimental, funny, have great action or even the formulaic plot-twist right at the end, and that is fine. What I love about Takashi is every time you watch one of his films it grabs you by the bollocks and drags you through the experience. It isnt always fun being dragged around by your nuts but by God its not something you ever forget. I love how extreme the experience of his films is and how no taboo is ever off limits. For me, film is art, art is about striking you and Takashi is the master of striking you. As is typical with Asian cinema, as well, the cinematography is always dynamite, although the plots are not necessarily.
Park Chan-Wook - For me, and I think Spoony and I disagree on this - Korean cinema has the best cinematography in the world. (I thought A Bittersweet Life was more beautifully shot than Ichi - although that is not Park's work - and he disagrees.) Park makes Korean cinema as beautiful as anyone, but in truth he represents a style common to a number of directors of his generation working in his country. Even the most (potentially) mundane objects can be shot to look like the most stunning sculptures. Park's work has some of the benefits of Takashi's work (or probably a lot of Japanese cinema in general) in that it is less formulaic than what is produced in the US and often grittier. However, it is (again, I think you can draw conclusions about Korean versus Japanese cinema in general, here) much more coherent, for those who like their films with a followable plot. I love Park in particular for the Vengeance Trilogy, which I think is brilliant, and in particular Old Boy.