Jesu Joy of Man's Desiring - Bach
Pachelbel's Canon in D
The Moldau (Vltava) - Smetana
La Rejuissance (The Joy) from Music for the Royal Fireworks - Handel
Messiah - Handel
Eine Kleine Nachtmusik - Mozart
Just to be pedantic, not all "classical" music is actually classical. Classical refers to a very specific period of time ranging from 1750-c. 1820. Beethoven, Mozart, and Haydn are considered to comprise the Viennese classical school. Brahms, Schubert, and Mendelssohn also wrote some works that are considered to be more classical - they are cross-overs between classical and romantic.
Music written after the Renaissance but prior to 1750 is usually classed as Baroque. Handel and Bach are two of the most famous Baroque masters.
Music written from 1820-1900 is considered Romantic. Schubert, Schumann, Mendelssohn, Dvorak, Greig, Tchaikovsky, Brahms, Chopin, Liszt, Verdi, Wagner, and Rachmaninoff are among the Romantic composers.
From 1900 onward much "classical" music falls into the Post-Romantic and Impressionist styles. Debussy and Ravel are Impressionist composers. I believe Mahler is considered more Post-Romantic.