Free Classical Music Archive
Phonoarchive has a large and random collection of classical music available to download, mostly in MP3 format. I know what you're thinking - you don't know very much about classical music. Why not sample some for free? I'll make just a few recommendations.
They have all 16 Beethoven String Quartets (my favorite is No. 13, Opus 130 in Bb). If you're up for something a bit challenging, Bartok's Music for String Instruments, Percussion and Celesta is well worth hearing. If you prefer something more contempletive, you can't go wrong with Bach's Das Wohltemperierte Klavier. In the mood for something melodramatic? You really can't beat Verdi's Requiem for sheer bombastic choral spookiness. If you'd like something fluffier, Haydn wrote a huge number of symphonies which all pretty much sound the same to me, but they are pleasant enough on the ears. I am especially fond of Schubert so I'll recommend his Death and the Maiden quartet as a good starting point. His Piano Sonata Opus 143 in A Minor is also quite beautiful, and you should hear what is probably the most famous of his lieder, Der Erlkonig. Finally, skip Vivaldi's overplayed The Four Seasons and check out his Oboe Concertos, which are a lovely example of baroque delicacy.
Perfomance matters a lot in classical music (the reason I'll often have three or four different records of the same piece) and these recordings are of unkown provenance. But you can't sneeze at free music!