There are lots of excellent responses here regarding what makes a good conductor; though the ideas are also somewhat subjective. For me, classical music is supposed to be fun. I hate the term "classical music appreciation". What about "classical music enjoyment"? In this sense, I think that early Leonard Bernstein (back in the 1950s, 60s and 70s) is my gold standard; and Bernstein was great practically across the repertoire. In those recordings that he did with Columbia Records and almost always with the New York Philharmonic Orchestra, Bernstein really knew how to unlock the flavor; how to make the orchestra swing. Bernstein's Haydn was unbounded joy. His Mahler and Shostakovich, vibrant and intense. His Beethoven and Brahms, solid and strait-forward. Bernstein's Copland is good fun; the best (maybe even better than Copland's own recordings of Copland).
Later, when Bernstein switched over to DG in the 1980s and divided his time mostly between the New York Philharmonic Orchestra, the Vienna Philharmonic Orchestra, and the Israel Philharmonic Orchestras; Bernstein took on a more introspective bent, slowing things considerably, as if trying to concentrate on every note and every morsel of goodness. Sometimes this worked and sometimes it didn't. I thought Bernstein's slow approach was OK for Tchaikovsky, Sibelius, and Mahler; I thought that it didn't do very much for Beethoven and just sucked the life out of Brahms.
Dynamics are, of course, very important; and it must be difficult to play the orchestra in a way that is not too loose and not too tight; not too soft or too loud. Everything should be well-measured, as with cooking a meal. Too much spices and all you taste is spices. Too little spice and the food tastes like nothing. In this sense, George Szell (who was also a gourmet chef) seems to be very aware of getting the balance just right in his recordings. And while some of Szell's recordings are beautiful beyond measure (His Mahler 4 with Judith Raskin; or Mozart's Sinfonia Concertante and Clarinet Concerto with in-house musicians); Szell's approach sometimes sounds a bit too regulated and lacking in warmth.
There are lots of conductors that seemed to favor a very smooth and sonorous approach and that is good, sometimes. Bruno Walter's recording of Beethoven's Symphony #6 "Pastorale" is top-notch; as is Eugene Ormandy's very underrated and lyrical recording of Beethoven's Symphony #9 "Choral". When Ormandy died in the 1980s, I read an obituary that said he turned the strings to silver and the brass to gold; and that worked for him. Herbert Von Karajan, however, takes it too far sometimes when the shine that he places upon the music distracts from the feelings that the music is supposed to convey.
I always found Bernard Haitink to be a bit on the dull side; not that his recordings can be faulted in any way. A Haitink recording is almost always solid, but there's not much fun or "swing" to it compared to, say, Bernstein. Likewise, Colin Davis is almost always a bit too understated and reserved. Even so, Davis' approach does work in his favor in the case of Berlioz. In the Berlioz Requiem that he did with the London Symphony Orchestra and Chorus, Davis gets it just right as his sense of restraint and English polish does well to allow Berlioz to speak for himself, as I think Berlioz is very easy to over-play. Berlioz was as classically minded as he was a wild Romantic. So sometimes the right approach for one composer may be the perfectly wrong approach for another and vice versa.
I don't like the recordings of conductors that are too theoretical, and there are many in the realm of HIP recordings, and I always found my thoroughly un-HIP recordings by the likes of Bernstein, Ormandy, Szell, Walter, Reiner, Stokowski, Toscanini, Mitropoulos, and even Karajan, to be so much more fun, dramatic, and interesting than the brisk and detached HIP conductors whose individual styles don't seem to have the same presence as the above mentioned gallery of conductors who, like it or not, each had some type of personality. The HIP conductors, on the other hand, seem to be too caught up in the theory as to "How Vivaldi would have wanted it played", and to me, the "theory" is so much less fun (and just as valid) as Sergiu Celibidace's Zen approach to Bruckner, or Stokowski's free bowing, or Karajan's slick approach, or Furtwangler whose approach defies description. Masaaki Suzuki and Jordi Savall might be exceptions regarding my generalization on HIP conductors; but to me, most other HIP conductors sound much like one another, and to this day, HIP recordings make up a comparably small part of my music collection.
A good conductor should support new music. While I've found Pierre Boulez to be among the more cool and calculating musicians who were a bit too reserved for my inclinations: I always respected Boulez' championing of composers such as Varese and Schoenberg; and it was through Boulez' recordings that I got to know the strange realms of those Ultra-Modern composers. Along the same line, conductors should bring forth the music that reflects the heritage of the country to which they serve. In this sense, Gerard Schwarz has done very well to bring the likes of William Schuman and Walter Piston to the fore; as has Marin Alsop done justice to the music of Samuel Barber, Roy Harris, and Leonard Bernstein. We need conductors in the USA to program music by Americans of various races, ethnic groups, cultural backgrounds, and of both genders; and preferably those among the living; even if it most of it can't possibly be compared to the Grand Old Dead Men of Europe.
A great conductor should LOVE the music; which brings us full circle back to Leonard Bernstein. One can clearly see in Bernstein's rehearsals and lectures that he LOVED the music. He had many things to say about the music; some of it was profound, some of it was pompous, and some of it was just plain wrong. The man was prone to reading too much into the music; but whenever Bernstein spoke about the music; he was always speaking with great love and enthusiasm; and I think that comes out in a Bernstein recording.