who is the greatest living conductor of standard repertoire?

There is nothing more futile than wondering who is the "greatest" in classical music, whether it be composers,conductors, instrumentalists or singers. People tend to equate the most famous with the greatest, but just because musician X is more famous than musician Y does not necessarily mean that X is the greater one.
Claudio Arrau never capured the public imagination they way Horowitz did, but he was never as flashy a performer. Yet he has always struck me as a more profound and penetrating interpreter of the piano repertoire than Horowitz.
There is absolutely no lack of great conductors today, despite the many fans who long for the "good old days", and there are some very talented young conductors who are beginning to gain international recognition, and have great potential.
Any age that has the likes of Abbado,Ashkenazy,Alsop, Bychkov,Barenboim,Blomstedt,Berglund,Boulez,Belohlavek,
Chailly,Conlon,Chung, Dutoit, Dohnanyi, Colin and Andrew Davis, Eschenbach,Elder, Ivan and Adam Fischer,Gergiev,Gardiner,Gielen,Haitink,Harnoncourt, Inbal, Neeme and Paavo Jarvi, Jansons,Janowski,
Levine,Luisi, Muti,Mehta,Maazel,Mackerras,Masur, Nagano,Norrington,Noseda, Ozawa,Previn, Pappano,Pesek,
Rattle,Rozhdestvensky, Slatkin, Salonen,Segerstam, Thielemann, Thomas, Temirkanov, Vanska, Weler-Most, De Waart, and Zinman, to name only some, has nothing to be ashamed about.

The whole concept of choosing a 'greatest' of anything in western classical music is flawed, in my opinion.  There are many conductors active today who have moments of greatness and the pleasure is in being able to enjoy each and every one of them through their live performances and/or recordings.

My favourites include Simon Rattle, Riccardo Chailly, Antonio Pappano, and Colin Davis.  I would struggle to choose one of these as a 'No.1' and, indeed, the choice could easily be confused further by recalling several more names.  Furthermore I would have to choose different favourites depending on the repertoire being discussed.  For Berlioz and Dvorak, Colin Davis would be my choice but in Mendelssohn and Brahms I have a special place for Chailly's approach.  For Beethoven there are several recordings I would struggle to live without, but ultimately I would have to go back to a long deceased conductor in the shape of Klemperer.

The beauty is in the variety and reducing such things to charts and polls does the music and it's interpreters an injustice.

[quote=superhorn]Abbado,Boulez, Colin Davis,Ivan Fischer,Gergiev,Haitink,Harnoncourt, Jansons,Janowski, Levine, Muti,Maazel,Mackerras,Rattle,Rozhdestvensky]

I have reduced Superhorn's lists of "greats" to fifteen and still feel I'm being generous with the word "great". I would say that an age which produces half a dozen is already exceptional. (As an example from a previous generation: Toscanini, Walter, Klemperer, Furtwängler, Erich Kleiber, Fritz Busch.)

Not 'always', sadly - eg, Karajan's 1970 version of Bruckner's 4th was recorded in the Philharmonie, and his 1957 Bruckner's 8th in the Grunewaldkirche, both on EMI.  

And, after the Berlin Phil stopped using the Jesus Christus Kirche for recording in 1973, he recorded a complete series of Beethoven symphonies in the Philharmonie for DG  in the 80s.

Everything I've heard from Pappano has been terrific, and I wish he was recorded more.

Of course, we're not officially allowed to call any conductor "great" unless they've been dead for 50 years.

I think this is an impossible question, though a very stimulating one. But living in a country that is far away from most important musical centers, I have often given serious thought to the question, What conductor would make me take a long trip just to listen to him? In standard repertoire I would travel to listen only to those that take risks and give characteristic and unforgettable performances. I have actually done this for Muti, Abbado and Rattle, and I am looking for a place and date where to go to attend a Harnoncourt concert. I did enjoy very much my trips to listen to those three conductors, but the most rewarding was Muti. 

I just recently traveled across the U.S. to see Haitink conduct the Chicago Symphony in the Beethoven cycle that they are doing. Rather risky but absolutely first-rate performances. They have unhinged my molecular structure. I would not have expected Haitink to takes risks at this age, but he is, and he's getting away with it. Anyone who can take the now somewhat cliché 5th and make it sound fresh no doubt carries the mark of greatness. Then again, it is irrelevant to say he is the greatest. It de-emphasizes the importance of the music. It is important to remember that it is not a competition (though H. v. Karajan may have disagreed).