I’ve become a classical nut over the past couple of years, but couldn’t really get into some composers’ works despite listening to several of each. Could anyone enlighten me as to the best introductory pieces by Mahler, Sibelius, Dvorak, and Prokofiev?
Symphonies #5, #2, #9, #7, respectively.
I’m a big Mahler fan, and I recommend his first symphony. Of course, I like loud, bangy, dramatic music.
I’ll second MaxTheVool’s recommendation of the First as an intro to Mahler. (But my own favorite of Mahler’s works is Das Lied von der Erde.)
Dvorak’s 9th Symphony, “From the New World” is a great introduction to his work.
And I’ll throw another vote in for Mahler’s First. I especially like the 3rd movement.
From a chorister’s point of view it’s pretty hard to beat Mahler’s Symphony No. 8
For Sibelius, I recommend the violin concerto.
In addition to the ones mentioned:
Symphony #4 is a wonderfully light but not ‘fluffy’ piece. (Great to sing along with if you are a soprano).
Das Lied von der Erde (Song of the Earth) - One of my favorite musical passages: Dunkel is das Leben, ist der Tod. Damn, sometimes I wish I was born a tenor, just to sing this cycle (although I did hear a baritone do a far more than passable job on this - definitely needs emotion and power to these pieces to do them justice, as well as a very competent accompanist, or better yet, orchestra). S’wonderful. Gotta get another copy.
Kindertotenlieder (Songs on the Death of Children) - This is The Wreck of the Edmund Fitzgerald of the classical world. Almost guaranteed to suck the life out of any party and send your guests home early to fold road maps or do something fun. Other than that, it’s a great piece to study. Very depressing both lyrically and musically, especially if you also read the Rueckert poems that Mahler did NOT set to music. Hoo boy, you can really feel for Rueckert.
Das Knaben Wunderhorn (The Youth’s Magic Horn) almost like min-Grimm’s Fairy Tales. A few of my favorites:
[ul]
[li]Um schlimme Kinder artig zu machen [/li][li]Des Antonius von Padua Fischpredigt [/li][li]Wer hat dies Liedlein erdacht? [/li][li]Lob des hohen Verstands [/li][/ul]
Personally, my favorite Mahler vocalists: Elly Ameling and Dietrich Fischer-Dieskau (almost I will listen to other suggested artists with open ears).
I think Mahler’s 4th Symphony is the most accessible.
http://www.netaxs.com/~jgreshes/mahler/works_list.html for info on Mahler.
Exactly what I was going to say.
And of course, please add the word Mahler is 'twixt the “Ooooooooooooh” and “my” in my post.
Recommended recordings:
Dvorak: Symphonies 7 & 8 - far superior to the ninth, IMO
Mahler: Das Lied von der Erde, with Kathleen Ferrier - unbeatable.
Sibelius’ violin concerto played by Oistrakh
Holy string-of-universally-unacceptable-words! How did I completely miss THIS one over all these years!?!? Thank you very much for bringing this to my attention!
You wouldn’t go wrong with tdn’s suggestions, but here are a few alternatives:
Mahler: his first symphony was my introduction to him and made me want to hear more. Either it or the 5th would make a good starting point, especially if you, like myself, prefer his purely instrumental compositions to those which include vocals.
Dvorak: the 9th (“New World”) symphony was my introduction to him, and it may well be his most popular and easily accessible work, and it’s what I’d recommend as a starting point. Unless you’re particularly fond of cello and/or violin concertos: he wrote a good one of each. Or if you like light, lively, bouncy music, check out his (orchestrated) Slavonic Dances. Or if you prefer chamber to orchestral music, start with the “American” String Quartet or the Piano Quintet.
Prokofiev: “Peter and the Wolf” is probably many people’s intro to Prokofiev. It may be the first thing of his I heard, but the first thing I really remembered hearing, that knocked my socks off, was his 3rd Piano Concerto. You might also wanna try his ballet music for Romeo and Juliet—part of the great tradition of Russian ballet music that includes both Tchaikovsky and Stravinsky (and falls in between them musically, having something of the former’s melodic accessibility and some of the latter’s edge).
Where were half of you people in my classical music threads? 
Latest one: Symphony #5. Snobbery not required.
As to the OP: I think Mahler’s First Symphony is a better introduction than the Fifth, but maybe that’s because it’s his first work I ever heard. Prokofiev can be a little weird to the uninitiated ear in general, but I agree that his “Peter and the Wolf” is probably the best work to start with. The same goes for Sibelius, as the unusual harmonies and sometimes lack of melody can render his works almost unapproachable. The latter two can be very much an acquired taste, but once you acquire it, you’ll wonder how you did without it.
Most of Dvořák’s works have a much stronger Eastern European flavor to them, which is probably why his most famous one is the one least like the others.
On the other hand, he has some extremely accessible shorter works, notably the Karelia Suite and Finlandia.
In defense of my own choices,
Mahler’s 5th is the first I ever learned (and memorized). But I love the 3rd and 4th as well. The problem with Mahler is there is no kiddie pool to get your feet wet. You pretty much have to dive right into the deep end. But I love the 5th because the first movement is so dark and heavy, and yet so… German. And the Andantino is one of the most important works you’ll ever have in your collection.
For the Dvorak, I picked the 9th because it is the Stairway to Heaven of the classical world. I’m not a huge Dvorak fan, so I didn’t put any more thought into it than that.
Prokofiev is hard. I like the 7th because it has a fascinating history. But for an introduction, I should have said Dance of the Capulets from Romeo. Extremely accessible and fun, and not a huge time commitment.
As for the Sibelius, it is quite simply the best music written, ever, period, indisputable fact. And I’m willing to back that up with fisticuffs. 
And be sure to find a copy of the film version of Death In Venice. They used Mahler for the soundtrack, and the movie is just staggeringly beautiful anyway.
For Prokofiev, I’d steer you towards the First Symphony (aka the “Classical”), the Lt. Kije Suite, and the The Love for Three Oranges Suite (the full work can be saved for later). The Fifth Symphony is also a winner, and fairly accessible.
If you’d like some vocal in the mix, try his Alexander Nevsky (music written for the movie directed by Eisenstein).
I was going to mention the Piano Quintet. I fell in love with the piece when I first heard it live, with Itzaak Perlman among the players.