[Solatar]

Everybody's got all the famous and badass 19th century loud Romantic stuff pretty much covered.  Here's some more pretty stuff I really enjoy (you might like it if you like the Barber Adagio).  Picked the version of the Palestrina and the Mendelssohn concerto for the specific artists recording it, but the rest were just decent videos I found on youtube.

Missa Papae Marcelli - Giovanni Perluigi di Palestrina <--underrated but gorgeous, this is also my favorite recording (it's from 1980, but all the more modern ones I can find rush the hell out of this piece).  Traditionally this was the piece that convinced the Council of Trent not to outlaw polyphony on the grounds of not being able to understand the words, and if you follow along with the Latin all the words are easily recognizable, unlike most Renaissance polyphony.
Fratres for String Orchestra and Percussion - Arvo Pärt - it's serialism, so it's mostly mathematical, but it's awesome to listen to to see what kinds of phrase/melody patterns your brain INSISTS are there.
Cantus In Memory of Benjamin Britten - Arvo Pärt again, but a slightly different style.


And just because I think the world would be a better place with more Schubert and Mendelssohn:
Unfinished Symphony (1st mvt.) - Franz Schubert
Hebrides Overture - Felix Mendelssohn
Mendelssohn Violin Concerto - Itzhak Perlman and Daniel Barenboim (it's in two parts on youtube, but it's worth it for these two artists)

[Flipside]

Night on Bald Mountain - Mussogorsky - http://www.youtube.com/watch?v=iCEDfZgDPS8
The Sabre Dance - Aram Khachaturian - http://www.youtube.com/watch?v=gqg3l3r_DRI

A couple of favourites that have stuck with me for decades

[Mongoose]

Ha, that reminds me...I recently saw the Sabre Dance appear on an album of "Sensual Classic Songs" for sale on Amazon.  As someone in the comments put it, "...what type of sex are those people having?"

[Flipside]

Heh, almost forgot another one of my favourites, Canon in D by Pachelbel.

http://www.youtube.com/watch?v=NlprozGcs80

Sadly over-used by the BBC for every gardening or antique show out there, but still a lovely piece of music

[Solatar]

but still a lovely piece of music

Unless you play the cello.

EDIT: And how could I forget my favorite piece of music ever written.  This was one of the pieces that Joshua Bell played in the Washington subway during rush-hour a few years back. 

Chaconne from Partita No. 1 in Dm for Solo Violin - Bach/Itzhak Perlman
Part 1
Part 2
Who needs four violins for four part harmony when you have one violin with four strings?

Excerpts from Joshua Bell playing in Subway

[Flipside]

but still a lovely piece of music

Unless you play the cello.

Heh, true, not the most musician-friendly tune out there But then, look on the bright side, if you played flute, your hallmark is Flight of the Bumblebee

http://www.youtube.com/watch?v=LI3wIHFQkAk

[deathfun]

I know it's cliched these days, but I still love Barbers Adagio for Strings, did so long before Homeworld came out. It was written as a Eulogy to his Father and is just such a powerful piece of music.

Damn, forgot to mention that one
Was listening to that song off the classical CD I have long before I knew how to do math

[Axem]

Oh yes nearly forgot

Vassago's Dirge - Joel Reimer

Oh, you're much too kind!

There's just too much to list for me, so I'll try to list up some not mentioned so far (but I'll just give a repeated shout out to the entirety of Dvorak's 9th Symphony, which is super kewl).

Rachmaninov - 2nd and 3rd Piano Concertos (I don't need to explain myself there!)
Tchaikovsky - 1st Piano Concerto (especially that first movement!)
Mahler - Symphonies No 3 and 6
Ravel - Bolero
Nielsen - Symphony No 4
Berlioz - La damnation de Faust

And some more Piano specific ones
Beethoven - Moonlight and Pathetique Sonatas
Chopin - Nocturne in B major
Schubert - Piano Sonata No 16

[karajorma]

Ha, that reminds me...I recently saw the Sabre Dance appear on an album of "Sensual Classic Songs" for sale on Amazon.  As someone in the comments put it, "...what type of sex are those people having?"

Wait for someone to Rule 34 that one.

[Nuke]

some years ago i downloaded a taped performance of wagner's ring cycle, complete with subtitles so i could follow the plot. that was the longest thing ive ever watched. though the experience was not entirely regrettable, i very much doubt il ever do it again.

[Thaeris]

Here, have some Satie:

Gymnopedie No. 1