The Nutcracker, by Petr Ilyich Tchaikovsky
The Nutcracker is a Christmas staple in my family. We began by watching movie and television versions with the kids when they were tiny, and then this year we brought them to their first live performance, by the Boston Ballet. They were mesmerized, and have requested music from the ballet as bedtime music on a regular basis ever since. There are also many beautifully illustrated children's books telling the story - the one illustrated by Maurice Sendak is a particular favorite of mine, and fun to read before watching the Pacific Northwest Ballet's version, for which Sendak designed the sets.
Even apart from the context of the story and the ballet, however, the music is complex and interesting, with memorable melodies and rhythms, and wonderful use of featured instruments for specific themes.
The Magic Flute (Die Zauberflote), by Wolfgang Amadeus Mozart
The Queen of the Night with Rene Pape's rich bass in "O Isis and Osiris". And what child would not be tickled by Papageno and Papageno's funny duet preceded by a trio of young boys who sing while flying (or at least, in this particular version, sitting on the shoulders of "invisible" puppeteers). Many recordings are available in English as well as the original German. The Metropolitan Opera's version, directed by Julie Taymor (of Broadway's The Lion King fame), is particularly accessible to children, because of its use of full-size puppetry (the bears! the witches! the food!) and flying, as well as marvelously fantastical costumes and sets.
Music for the Royal Fireworks, by George Frideric Handel
Piano Sonata No. 14 in C# Minor (The Moonlight Sonata), by Ludwig van Beethoven
The Barber of Seville (Il Barbieri di Siviglia), by Gioachino Rossini
The Rabbit of Seville". It's brilliant and funny, and pairs Rossini's catchy melodies with typical Looney Tunes silliness. But the original opera supplies plenty of silliness as well, while retaining all those catchy melodies and adding in brilliantly trained vocalists as well as elaborate and colorful costumes and sets. Rossini's opera is based on the first of three plays written by Pierre Beaumarchais centering around a barber named Figaro (several other composers wrote less successful operas based on the same play; Mozart based his hugely successful opera "The Marriage of Figaro" on the second of the three plays). The plot is a complicated and confusing affair involving disguises, illicit love affairs, gossip, and bribery - all the usual opera devices. Figaro's opening aria is not only one of the most well-known to non-opera fans (again, largely due to Bugs Bunny), it's also really fun to sing along on the "lalalala" parts even if you don't know the Italian lyrics.
The Overture to "Candide", by Leonard Bernstein
If you do decide to watch the full version, I highly recommend the semi-staged Great Performances special on PBS, which starred Kristin Chenoweth and Patti LuPone, among others.
The Liberty Bell, by John Philip Sousa
The march is also an excellent example of the standard march form that Sousa often employed, AABBCDCDC, so it can serve as a easily understood music theory lesson. On the linked recording, the initial A section repeats at 1:06; the B section begins at 1:22, with a quiet section featuring flutes and clarinets which is repeated more loudly by the brasses at 1:37; the C section begins at 1:53 with another quiet, more legato section; section D begins with the clanging bell at 2:26; at 2:51 we repeat C; at 3:23 we're back to D and the clanging bell; and finally at 3:48 we hear a brassier rendition of the C strain with the bells included to complete the march.
Carmen Suite #1, by Georges Bizet
"Habanera" being sung by an animated orange on an episode of "Sesame Street." As well as the "Habanera," most of us recognize "The Toreador Song" (and probably sang it with the lyrics "Toreador-a, don't spit on the floor-a, use the cusipidor-a, whaddaya think it's for-a"). The music included in the suite range from fiery, fast-moving numbers to sweet, quiet waltzes and peppy folk dances.
The Four Seasons, by Antonio Vivaldi
Written as a series of four violin concertos based on each of the four seasons, Vivaldi included a series of poems (it is not clear if he was the author or not) clarifying the elements of each season that inspired his music. This is one of the earliest and most detailed instances of "program music," which includes a story or narrative aspect. My children are fascinated by the recording including the poems, recited by Patrick Stewart (you can listen to "Winter" with Stewart's narration here). These pieces are a beautiful example of music depicting an event and an emotion, and it's a great discussion for kids to analyze what different instruments bring to mind different feelings, or create different images.
Carnival of the Animals, by Camille Saint-Saens
In the Hall of the Mountain King, by Edvard Grieg
The Planets, by Gustav Holst
I could probably add 100 other pieces to this list, but I'll add links to just a few more that are worthy of inclusion. Happy listening!
The Brandenburg Concertos by Johann Sebastian Bach
The Minute Waltz by Frederic Chopin
Claire de Lune by Claude Debussy
The 1812 Overture by Petr Ilyich Tschaikovsky
Piano Concerto No. 3 by Sergei Rachmaninoff
Horn Concerto No. 3 by Wolfgang Amadeus Mozart
Rhapsody in Blue by George Gershwin
La Donna e Mobile (from Rigoletto) by Giuseppi Verdi
Flight of the Bumblebee by Nikolai Rimsky-Korsakov (for an even more fun rendition, listen to The King's Singers' brilliant vocal version - and stay listening for their version of The Barber of Seville overture that follows)
The Typewriter and The Waltzing Cat by Leroy Anderson
Funny Cats' Duet by Gioachino Rossini
Hungarian Dance No. 5 by Johannes Brahms
The Trout Quintet by Franz Schubert
Liebestraum by Franz Liszt
Tritsch-Tratsch Polka by Johann Strauss II
Toccata and Fugue in D Minor by Johann Sebastian Bach
Okay, that was more than a few - but it's still hardly scratching the surface of all the wonderful, accessible classical repertoire that's out there. So start listening!!