I can go for hours on this. Actually, the composers you named aren't necessary what I listen to as of now. I like Wagner's use of leitmotifs (a theme for each character) and his amazing way of not resolving chords for many minutes later. I also like Bach's strict counterpoint and slick chord progressions. However, Beethoven and Mozart seem very bland, transparent, and too "pop"ish, though very memorable.
"Classical" is such a broad term, though. But, these composers I'm mentioning are usually considered in that genre, even though some of them are still alive today.
My favorites are Stravinsky, Varèse, Bartók, Debussy, Schoenberg, Messiaen, Mahler, Holst, Partch, Penderecki, Schwantner, Crumb, etc (I always forget some). All of these I like for different reasons, on which I can go about for hours.
Stravinsky is just amazing in all levels because he does everything. I completely disagree on his statement that music is just to create an order in things. He was one for "neo-classical" music (meaning no emotion). That's why I hate when people say someone is a "neo-classical" band. Listen to The Rite of Spring and L'histoire du Soldat. I had a professor tell us once that if you listen to The Rite of Spring everyday you will become a better person. The piece just has everything; beautiful interweaving lines, lush orchestration, intense tutti sections, odd times, and powerfully simple melodies when necessary.
Varèse is one of my favorites mostly for his use of awesome dissonances and how he writes for winds. A lot of my small ensemble pieces sound like his as I like to take one motive and keep developing it slightly and twisting it around, sort of like looking at a sculpture from different angles. I love his orchestral work, Arcana, and his chamber pieces like Intégrales. Actually, I think I've heard everything he's ever done, since his surviving œuvre is so accessible and minimal, and I love it all.
Some people I love for just their orchestration, like Debussy, Mahler, and Holst.
Partch is one of a kind; I was/am a member of the official Harry Partch Ensemble. Crumb writes some of the most ridiculous stuff ever. His piece Black Angels - Thirteen Images From The Dark Land (such a metal title) is so scary.
I can talk more about this stuff if you have any questions.