We are limiting ourselves to one director per composer, so you can't mention Steven Spielberg, Oliver Stone and George Lucas for John Williams for instance, you have to pick only one director per composer.
My top 10 living composer-director collaborations (limited to one director per composer) are:
John Williams and Steven Spielberg
Howard Shore and David Cronenberg
Joe Hisaishi and Takeshi Kitano
Michael Stearns and Ron Fricke
Ennio Morricone and Giuseppe Tornatore
Vangelis and Ridley Scott
Thomas Newman and Sam Mendes
James Newton Howard and M. Night Shyamalan
Elliot Goldenthal and Neil Jordan
Hans Zimmer and Christopher Nolan
I am not a big fan of Elfman/Burton, Silvestri/Zemeckis etc even if I like some of their collaborations, they have too many misses - both film-wise and score-wise.
The most promising "new" composer-director collaboration for me is Jonny Greenwood and Paul Thomas Anderson, it is the probably most interesting "new" one since Howard Shore and David Fincher. I like Reznor & Ross's work for Fincher in general, but don't find it as interesting/imaginative/exciting as Shore and Fincher were in general. Even more recently I liked Mica Levi and Jonathan Glazer - that could be a promising one if they keep working together. I also really liked Yoko Kanno and Hirokazu Koreeda's Our Little Sister even if that was traditional score.
What would your top 10 living composer-director collaborations be?
Carter Burwell/Joel and Ethan Coen Patrick Doyle/Kenneth Branagh Danny Elfman/Tim Burton Michael Giacchino/Brad Bird James Newton Howard/M. Night Shyamalan Joe Kraemer/Christopher McQuarrie Theodore Shapiro/Jay Roach Alan Silvestri/Robert Zemeckis John Williams/Steven Spielberg Fernando Velazquez/Juan Antonio Bayona
Some of my favorite composer/director collaborations that are still going strong today:
Pino Donaggio / Brian De Palma (probably my favorite) John Williams / Steven Spielberg (of course) Ennio Morricone / Giuseppe Tornatore Francis Lai / Claude Lelouch (have been collaborating off and on for over 50 years) Philippe Rombi / Francois Ozon Abel Korzeniowski / Tom Ford Jonny Greenwood / Paul Thomas Anderson Angelo Badalamenti / David Lynch Carter Burwell / Todd Haynes Danny Elfman / Tim Burton (mostly because of their collaborations from 1985-1999)
If anyone is interested, there's a newly released Classic FM book about director-composer relationships. I don't have the book so I can't comment on it...