Kelly,
This is a really TOUGH one. There may not be much "new" classical music written these days, but trying to pick out the top ten from four or so centuries of great music is very difficult, at least for me.
However, given the criteria, here's my take:
1. Beethoven Symphonies--no classical fan should be without all 9 of these. Unfortunately, you can't get them on just ONE disk. Everyone should have at LEAST symphonies 3, 5, 6, 7, and 9.
There are MANY complete recordings out there, but I think Herbert von Karajan/Berlin Philharmonic on Deutsche Grammophon (1963 version) would be an excellent choice--not the most "modern" instrumentation, but inspiring and well-recorded for the time, as well as a good value in its CD reissue.
2. Felix Mendelssohn--"Hebrides Overture": I include this because it is one of my absolute favorites and is a great example of tone painting. Mendelssohn wrote this while on a trip to Scotland as he travelled out on the coastline to Fingal's Cave, near the Hebrides Islands. You can practically hear the waves lapping up against the boat in the music. My favorite recording of this is with Claudio Abbado and the Berlin Philharmonic (Deutsche Grammophon, 1985). The recording is excellent for the time.
3. Brahms Symphony No. 4--Brahms wrote only 4 symphonies and this one is his best, in my opinion, although they are ALL great. Leonard Bernstein conducting the Vienna Philharmonic on Deutche Grammophon gives a spirited reading. Brahms may have been the best at taking a simple motive (a musical idea) and making an entire movement out of it, as he does so spendidly in this symphony. The melody in the first movement is one of my all-time favorites.
4. "Luciano Pavarotti Arias"(London/Decca, 1982)--an aria collection sung by the "King of the High Cs". This one shows Luciano's voice off in his prime, and it includes probably my favorite aria of all time--"Nessun Dorma". Although perhaps other tenors are more refined musically in their singing (Domingo, for instance), no one sings with more exuberance and lyricism than Pavorotti.
5. Rachmaninoff Piano Concerto No. 3--I am a pianist by training and Rachmaninoff represents the epitome of romanticism at its pianistic height. The 3rd concerto is his best in my opinion, although many favor the 2nd. I would have a tough choice making a decision on which recording of this I would choose, as there are many good ones. Vladimir Horowitz on RCA Red Seal 24/96 audiophile recording is a remastering of the 1978 live recording, which was a MAJOR event in the world of classical music. Horowitz, the acknowledged pianistic master of romantic music in the 20th century, makes a return to the stage after a 25 year haitus (although he did record some during this time). Horowitz knew Rachmaninoff personally, having spent much time playing this concerto with him (2 pianos with Rachmaninoff playing the orchestra's part--Rachmaninoff himself was a phenomenal concert pianist), and it shows. This is one of the most emotionally-charged recordings ever made, and the 24/96 remastering does much to make it sound like the original vinyl pressing (which I have also). Having said this, I just recently purchased the Volodos/Levine/Berlin Philharmonic version of this concerto on Sony Classical SACD (its available in CD also), and the playing on this disk is VERY musical (probably more musical than Horowitz's), though not as emotionally-charged. The sound of this disk is the most GORGEOUS I have heard to-date from SACD. If all SACDs would sound this good (many recent releases are approaching this), I'd have a hard time going back to regular CD.
6. Dvorak Symphony No. 8--Giulini/Royal Concertgebouw Orchestra/Sony Classical, 1991. Giulini is one of my favorite conductors (along with Bernstein, von Karajan, and Abbado), and his version of this symphony is tastefully done here. Although many favor Dvorak's 9th ("New World"), I like the 8th better. Probably there are better versions out there (I have an older version on vinyl with Barenboim/Chicago Symphony that I love), but this one 'ain't shabby, and its recorded using Sony's super bit mapping, which gives a nice spacious acoustic.
7. Gustav Holst, "The Planets"--I have Charles Dutoit's Montreal Symphony on Londong/Decca version, which is brilliantly played. There may be better-sounding versions available but I would bet none better-played. This was one of the first classical works I became hooked on back in high school. Holst wrote one movement for each of the then-known planets (Pluto wasn't discovered yet). Program music at its best, and beautiful music even if you're not into keeping up with which planet you're listening to. I still enjoy this work after 25 years of listening.
8. Vaughan Williams, Symphony No. 2/The Lark Ascending, Andre Previn/Royal Philharmonic/Telarc--I LOVE Vaughan Williams' incorporation of English folk tunes (he was British) and sounds of the countryside into his music. You can practically picture the beautiful English hills while you listen. The 2nd symphony (I love his 5th also) is also somewhat programatic, having been written around the time of World War I. In the first movement you can hear the chiming of Big Ben and the pre-war calm, followed by the
the horrors of the wartime. The second movement is one of the absolute most GORGEOUS movements ever created for any symphony. As a bonus on this disk, you get "The Lark Ascending", which is one of Vaughan Williams' most beautiful tone poems, featuring a solo violin.
9. W.A. Mozart--no one should be without at LEAST one recording of Mozart's music. I would have a hard time deciding this one, as I would be torn between either his Symphony No. 40 in g minor (one of only two symphonies he wrote in a minor key--this one shortly after his father's death) or one of the many happy concerti he wrote for a number of instruments, particularly his piano conterti. I have a wonderful record (not CD) of Colin Davis conducting (I think) the Concertgebouw on Philips in the Symphony no. 40. I really need a new recording of this one on CD.
10. Chopin Nocturnes/Etudes--Being a pianist, no pianist would be without a recording of these. Chopin really revolutionized (as did Lizst) people's ideas of what the piano was capable of as an expressive instrument. I have played many of these in my studies and continue to enjoy both playing and listening to them today. Probably Arthur Rubenstein is the acknowledged 20th century interpreter of Chopin's works, although I don't own a recording of him playing these (another deficiency I hope to correct). Ashkenazy's recording of these for London/Decca is quite good, although it is on 2 cds!
Well, this is my list, assuming these would be the only 10 allowed. But there is SO much more I'd like to put on the list: Mahler's symphonies, Debussy's tone poems (especially "La Mer"), Bach's many wonderful works ("St. Matthew Passion", "Brandenburg Concertos", "Art of the Fugue"), and Brahms'/Mendelssohn's/Beethoven's violin concertos, just to name a few. Thankfully I'm not limited to just 10!
Since I've taken quite a bit of time to write this, one final comment: It is a real shame that much of the best classical performances of the 20th century were not optimally recorded. Much of the great performances by Bernstein, von Karajan, and the like, were recorded digitally (from the late 70s onward). Although I've heard some mighty good CD players lately that get rid of that digital harshness, I've not run across any player that can restore the missing harmonics and soundstaging acoustic (decay of sound) of these recordings. These missing sounds, unfortunately, are the sounds that rob classical music of its heart and soul. I don't think one can FULLY enjoy classical music without FULLY enjoying the nuances of the acoustic (that is, non-electrical--meaning NATURALLY-sounding) instruments it was (and is) written for. This is why many classical music lovers so appreciate what the high-rez formats (SACD, DVD-A) can do for modern recordings. Thankfully, some of the oldest stereo recordings have been (and hopefully will continue to be) remastered from the original analog tapes into hi-rez (witness the Sony/Columbia SACD reissues). Unfortunately, I don't see how this will be possible with the majority of recordings made after 1980 or so, as most were probably recorded digitally. Of course, I'm glad we have them at least in CD format, and hopefully some of these will sound better transferred to hi-rez (we shall see). I say all of this in the hopes that classical music will continue to be recorded, and in the high-rez formats, and with the same high-level of artistry that has been present in the past. I for one will be supporting this with my purchases!