I hope people won't get back into the debate about what "classical" music is; SMX had a long statement about that some time back, and I hope that he will rest it with that.
Among my favourite composers are Dvorak, Beethoven, Tchaikovsky, Mozart and Smetana. Some composers I can't stand are Bach, Schubert and Paganini (don't try to start a discussion on why I don't like them or why I should be open-minded towards them. I don't like the music they composed, and that's it). I am very indifferent towards people like Wagner. The music is not necessarily bad, sometimes even pretty good, but the ideology behind it is not my cup of tea (no, I am not confusing the nazi interpretations of Wagner's work with Wagner himself, I am talking about the ideology Wagner himself put into his music).
Among my favourite symphonies and comparable works are:
Symphony no 9: From The New World (Dvorak)
Symphony no 9 (Beethoven)
1812 (Tchaikovsyk)
Symphony no 6: Pathetique (Tchaikovsky)
The Moldova (Smetana)
There is a lot of other and less well-known stuff I really love, but this is pretty much a list of what I would recommend anyone to start with. They are easy to find and also really popular.