There certainly is a strong melancholic aspect in a lot of classical music, but I would not say it is the "vast majority". But maybe you mean something very different with "feel depressed" and "gloomy mood".
In any case this is not at all what "boring" means in my book. That would be my feeling if I would be presented with something superficial and thoroughly empty. And yes, that can be a depressing experience.
What kind of music does not have this effect on you [we know this already for some Mahler, Bach, Chopin..]?
I tend to lean towards more melancholic and sombre pieces rather than the lighter, more upbeat works from the baroque or Mozart era. However, I do appreciate what Théotime Langlois de Swarte brings to the baroque. His performances are elegant and melancholic yet still fresh and expressive.
I'm not a fan of opera or the works of Vaughan Williams, Debussy, Wagner, Sibelius, Walton, Berlioz, or especially Bruckner.
Right now, I'm listening to a recording of Bach's early cantatas and loving it, but Bach holds a special place in my musical heart.
Piano, I admire Horowitz, Pollini, and Argerich. But a friend introduced me to Cortot, Leschetizky, and Rachmaninoff (as a pianist), and I've come to appreciate their interpretations too.
I have enough of Beethoven’s symphonies; I know them inside out. And while I've tried his quartets, they're not really my thing, but I do like some of his early piano sonatas. Mozart's symphonies tend to blend together for me.
I'm a big fan of Rostropovich and have enjoyed exploring his recordings, which led me to discover Dutilleux's "Tout un monde lointain," a piece I consider a masterpiece.
I generally like cello concertos, from Haydn to Dutilleux.
20th century. I appreciate Prokofiev's concertos and sonatas, but not so much his symphonies. I also enjoy Gubaidulina's "Concerto for Viola and Orchestra" and - on the same album - Kancheli's "Styx" featuring Yuri Bashmet. Shostakovich's quartets, and concertos, especially by Rostropovich, Ibragimova and Argerich (Piano Concerto No. 1 in C minor for piano, trumpet & strings, Op. 35, another masterpiece). Penderecki’s Seven Gates of Jerusalem. Most of Lutoslawski’s work. Messiaen: Quatuor pour la fin du temps, the one with Janine Jansen on violin.
That's pretty much where I'm at in my classical music journey.