A little late to this discussion, but I'll offer something a little off
the path of all the worthwhile recs given so far.....Most of the works
mentioned do seem to fall in the time swath from the present day back
to the High Baroque of Bach et al.  I'd like to put a plug in for works
from the five hundred or so years before Bach (even farther back, if one
is so inclined).

What one can find in listening to works from the Medieval, Renaissance
and early Baroque periods are a pretty different approach to musical
interpretation versus that of the modern day symphony orchestra or chamber
ensemble.  For one thing, most of the music from that time is for voice,
perhaps in combination with instruments--which though often recognizable,
differ significantly in detail and playing technique versus today's
instruments.  Singing techniques as practiced then, the harmonic language
(when it existed), and even tuning constructs for the music are different.

Of course, if vocal music is not to a person's taste, there's still
plenty of instrumental music from earlier times that's available on disk
or performed by Early Music ensembles.  Much of the music will be of a
less extended nature versus a symphony or concerto movement, for it was
often focused on dance music and the birth of forms as the instrumental
sonata, which means the pieces are shorter and have different concepts
of musical logic and progression.

The Early Music repertoire also has one very important difference from
music of later (say, post-Beethoven) periods, and that is the prevalance
of improvisatory approaches to performance, ornamentation etc.  Because
earlier music was often written in less precise notation, the ability
to ornament and improvise has become a hallmark of performing this
repertoire, given proper training and scholarship into the practices of
those periods.  Whether some classical musicians find this to be a more
interesting way to show off their skills is something I'll leave to
others to discuss, but I would say that Early Music performers can have
as much in common with a jazz (or even pop) band as a modern symphony
orchestra.  Even in the generally horrid business climate of classical
music recording, early music albums are constantly being released and
new (old) composers and their works rediscovered and performed once
again, sometimes for the first time in centuries.  Meanwhile, the ways
in which music is performed of the later Baroque masters such as Vivaldi,
Handel and others is even being reappraised, and the results are often
quite a break from the "sewing machine" musicmaking styles of past
decades.

If that kind of description appeals to a person new to "classical" music,
then check out the wealth of music out there that comes from before
Bach's time.  Monteverdi, Tallis, Josquin, Biber, Purcell, Byrd, Cavalli,
Lully, Marais, Marini are some names to begin with.  And there's plenty
more, even from that old prolific standy, "anonymous".....

Bill H.