'The flight of the bumble bee' was written by Rimsky Korsakov.
However, just because a lot of classical music is old, this doesn't necessarily put it in the public domain as Royaly Free. So I am afraid that you are typically hit with the same rules as in pop or rock music. It is true though that you are more likely to find Classical Music on Royalty Free music compilations, but of course you will probably have to pay for those.
If you just want a general browse on classical music then visit any of the music download sites. If you want a clue as to what Classical Music fits different kinds of mood, then post back and I am sure you will get many suggestions for spcific moods.
COMPAQ something or other with 500Gb Boot Disk, 1Tb external Firewire Disk, 4Gb Memory and a super duper sound card, 19" TFT Monitor etc etc etc
Sony TRV33e : Sony TRV310e : Canon XM2
Sony Vegas Studio editions to v11
Remember, there is always more to learn than there is to teach.