I'll start things off with my list:

In no particular order:

1. Herbert von Karajan
2. Adrian Boult
3. Neeme Jarvi
4. Jean Martinon
5. Charles Dutoit
6. Georg Solti
7. Colin Davis
8. Riccardo Chailly
9. Gunter Wand
10. Richard Hickox
11. Vernon Handley
12. Bryden Thomson
13. Leonard Bernstein
14. Seiji Ozawa
15. Simon Rattle
16. Claudio Abbado
17. Charles Mackerras
18. Rafael Kubelik
19. Mariss Jansons
20. Pierre Boulez

That's my list. Now your turn!

Nice list! - Mine is slightly similar, again in no particular order:
1. Andre Previn
2. Thomas Beecham
3. Adrian Boult
4. Herbert von Karajan
5. Colin Davis
6. Andrew Davis
7. John Barbirolli
8. Neeme Jarvi
9. Simon Rattle
10. Leonard Bernstein
11. Georg Solti
12. Bernard Haitink
13. Fritz Reiner
14. Neville Marriner
15. John Eliot Gardiner
16. Claudio Abbado
17. Otto Klemperer
18. Zubin Mehta
19. Osmo Vanska
20. Alexander Gibson

You have a nice list also.

I will say that once you get more into English classical music (i. e. Bax, Bliss, Walton, John Ireland, Howells, Rubbra, etc.), you will soon realize how great and important Hickox, Handley, and Thomson have been to getting the word out of these composers.

Have you listened to many English composers besides RVW and Elgar?

Hey MI, I definetely plan to check out some more English composers at some stage - at the moment I just have mainly EE, RVW and a few CD's of Bax and Delius.
I like Elgar and enjoy the "pastoral" sound of RVW and Delius .
I have been checking out English composers on Amazon a bit lately - I was thinking of getting the Bax symphonies on Chandos and the Arnold symphonies on Naxos and have seen an interesting series of Boult conducting English composers on the Lyrita label: all may be future purchases when funds allow .

You should definitely checkout Finzi, Ireland, Bliss, and Howells. These composers, all very underrated by the way, are amazing.

1. Sir Georg Solti
2. Wilhelm Furtwangler
3. Herbert Von Karajan
4. Zubin Mehta
5. Yevgeny Mravinsky
6. Leonard Bernstein
7. Seiji Ozawa
8. Andre Previn
9. Lorin Maazel
10. Eugene Ormandy
11. Erich Leinsdorf
12. Sergiu Celibidache
13. Sir Colin Davis
14. Istvan Kertesz
15. Pierre Boulez
16. Simon Rattle
17. Fritz Reiner
18. Bernard Haitink
19. Otto Klemperer
20. Sir Neville Marriner

My most recent favourite rankings:

1) Yevgeny Mravinsky
2) Arturo Toscanini
3) Kirill Kondrashin
4) Carlos Kleiber
5) Wilhelm Mengelberg
6) Yuri Temirkanov
7) Eugen Jochum
8) Herbert von Karajan
9) Herbert Blomstedt
10) Karl Bohm
11) Wilhelm Furtwängler
12) Yevgeny Svetlanov
13) Valery Gergiev
14) Nikolaus Harnoncourt
15) Ton Koopman
16) Kurt Mazur
17) Bernard Haitink
18) Antal Dorati
19) George Szell
20) Ferenc Fricsay

I can't think of a way to put this in a given order...

1. Willem Mengelberg
2. Paavo Järvi
3. Osmo Vänskä
4. Paavo Berglund
5. Jukka-Pekka Saraste
6. Esa-Pekka Salonen
7. Leonard Bernstein
8. Michael Tilson Thomas
9. Leif Segerstam
10. Klaus Tennstedt
11. Seiji Ozawa
12. Riccardo Chailly
13. Colin Davis
14. Sergiu Celibidache
15. Fritz Reiner
16. Simon Rattle
17. Otto Klemperer
18. John Barbirolli
19. Richard Hickox
20. Vernon Handley

__________________
"Aufersteh'n, ja aufersteh'n
wirst du, mein Herz, in einem Nu!
Was du geschlagen
zu Gott wird es dich tragen!"
-Gustav Mahler

No order

Solti
Svetlanov
Neeme Jarvi
Mariss Janssons
Handley
Kubelik
Karajan
Haitink
Barenboim
Tabachnik
Rattle
Hickox
Paavo Jarvi

Some others probably...

Perhaps in some order:

Solti
Dorati
Celibidache
Svetlanov
Mravinsky
Harnoncourt
Haitink
Kubelik
P. Jarvi
Bernstein
Marriner
Abbado
Rattle
Karajan

and couple of others that I forgot to mention

1. Bernstein
2. Karajan
3. Toscanini
4. Szell
5. Reiner
6. Furtwangler
7. Klemperer
8. Jochum
9. Giulini
10. Koussevitzky
11. Mehta
12. Monteux
13. Ormandy
14. Solti
15. Munch
16. Ozawa
17. Haitink
18. Previn
19. Chailly
20. Dutoit