Syrinx is THE famous flute piece
good start! hehe!
What kind of music (what era etc) is your favourite?
Am trying to think of "most famous" type pieces but my brain is flagging, so will instead suggest some of my favourites that I think are well known enough to be easy to get hold of!!:
Bach - Partita in A minor
Bach - flute sonatas
Hadyn - flute sonatas
Telemann - fantasias
Mozart - flute concerti and the flute and harp concerto, also Andante in C
edit: oh and his flute quartets!
Debussy - PrÃ©lude Ã l'aprÃ¨s-midi d'un faune - not strictly speaking a flute piece, but very famous flute solo
Bizet - Entr'acte from Carmen - same deal as above!
Franck - flute sonata
Prokofiev - flute sonata (
Am surely missing some obvious ones here but some more to add to your list anyway