Many consider Stravinsky's "The Rite Of Spring" to be the most important piece of music written in this century.  Without a doubt it is among the most important, and if you like 20th century orchestral music, you should hear it.  Due to it's popularity there are several recordings.  I tend to lean towards the Pierre Boulez recording that also features Stravinsky's "Petrouchka".  There is also a recording available which has Stravinsky conducting the work himself.  There are even piano transcriptions available which shed new light on this groundbreaking work.
    Also in the realm of piano, there is the infamous recording of Maurizio Pollini playing "3 Movements From Petrouchka".  This recording is so amazing many reviewers have expressed concern for the safety of Pollini's soul (implying he had sold it to the devil).  If you're a piano nut like myself, you will LOVE this.
    Back in the wonderful world of orchestral music, there is "The Firebird".  This is an exciting multi-movement extravaganza which showcases the ability of the modern orchstra in it's full power.  While not everyone likes this style of music, those who do will not be disappointed by this work.  Again, I would suggest the recording with Pierre Boulez conducting.  The D major violin concerto is also a favorite work by this composer.  We see another side of Stravinsky here, a much more playful one.  In fact, those who do not like the harsh sounds of "The Rite Of Spring" or "The Firebird" may love this piece.