I find most of Bartók's music beautiful, some of it frightening, but all of it exciting, because he had a feeling for rhythm unmatched by any other modern composer, and that includes Stravinsky. In fact he had a feeling for rhythm that's only found otherwise among African and jazz musicians, and to me his nearest rivals are actually Charles Mingus and Duke Ellington. (It was rhythm more than melody that he collected on his field trips in Transylvania and Rumania).
In fact I first came to Bartók not through classical music at all, but because back in 1963 I read in a biography that Charlie Parker had liked his music, and so set out to hear some for myself. The piece that hooked me for life was the 2nd Violin Concerto heard on a cheap Hungarophon LP, but in later years I had the luck to hear it played both by Isaac Stern and by Itzak Perlman. I also saw George Solti's farewell performance, of the Concerto for Orchestra.
Bartók's opera Bluebeard's Castle is the masterpiece of Expressionist music-drama, but though I've seen it twice on stage in London I didn't find either production satisfying. The BBC's 1988 TV production with Robert Lloyd as Bluebeard is the best staging I've seen, and my favourite recordings are the Walter Berry/Christa Ludwig, the Fischer-Dieskau/Julia Varady and the 1999 Grammy-winner with Jesse Norman. I was in the Queen Elizabeth Hall in 2001 when the Emerson Quartet played all six of Bartók's string quartets in one evening, and if that sounds like cruel-and-unusual-punishment or pure machismo, actually it was sublime (I'll do it again given the chance).
Bartók (like Richard Strauss) chose not to abandon the directly emotional effects of Romantic harmony, but rather to push them into new territories -indeed his strange tonalities can sometimes make you feel what seem like wholly novel emotions. When I first acquired a portable CD player I discovered to my amazement that listening to Bartók in the open air is not only a great pleasure, but makes enormous sense of the music. To me there's something about the granularity of his rhythms and the way they interact with his harmonies that seem to "fit" the fractal aspects of nature - branching trees, mountain screes, scudding clouds, falling water. That isn't to say that it's in any sense "program music" - the effect is some kind of structural analogy rather than symbolism. If you don't believe me, try listening to the 2nd Violin Concerto on top of a mountain, or the Adagio from his 3rd Piano Concerto in the Burren in the rain. I keep a lot of his solo piano music, including chunks of Microcosmos, on my Palm Treo and often just sit on a bench on the Heath or Regent's Park to listen to two or three pieces.
Bartók lead an eventful life, dying in poverty-striken exile in New York, of leukemia, in 1945, the year I was born. That same year Charlie Parker played with Dizzy Gillespie, Max Roach and Bud Powell at New York Town Hall to great acclaim. Imagine that Bartók had met his admirer Parker (and had been able to communicate across the language barrier!) Then Charlie Parker with Strings might have taken Western music in a whole new direction.
"Coming out top", a 1994 review of Malcolm Gillies "Bartok Companion" by Paul Driver in the London Review of Books, is an informative essay in which Driver makes the case for Bartok's greatness. There's a very short and rare clip of Bartok playing a fragment from his 1911 Allegro Barbaro on YouTube here:
Here's a short extract from a recording of Zóltan Székely playing Violin Concerto 2 at its first performance in 1939:
And here's Martha Argerich playing the marvellous 3rd Piano Concerto:
Here's a selection of good Bartok performances as a Spotify playlist.
[I "painted" the Bartok portrait at the top of this page digitally (from a well-known photograph), using a Wacom Bamboo graphics tablet and PD Particles software].