Bach's Sonatas and Partitas for solo violin
Mendelssohn Violin concerto in E minor
Asturias(Leyenda)-Isaac Albeniz
Introduction et Rondo capriccioso-Saint-Saens
Beethoven's Piano Sonatas
Any good Russians- Shostakovich, Tchiakovsky, Prokofiev, etc. I like the ballet music of them all
Maurice Ravel and Rachmaninov
The "best" isn't necessarily the "nicest". Bartok's music such as "The Miraculous Mandarin" can hardly be described as nice - but what an amazing score!
"moonlight sonota" by beethoven
If you want something different why not try some modern composers such as Philip Glass
My personal favourite piece of music is his String Quartet No.5, particularly the last movement (the best part is around the 3 minute mark)
If you're into more 'traditional' classical music, I would suggest Mussorgsky's Night on the Bare Mountain, or Borodin's Polovetsian Dances from Prince Igor
Vivaldis' "Four Seasons" is very accessible to the first time listener. I also love the Bhrams Violin Concerto in Dminor. There is Beethovens' piano sonata no.14, the "moonlight sonata" which you have probably heard elsewhere already. Barbers' Adagio for strings is very stirring, as is Albinonis' Adagio.
On classical guitar, try the Rodriguez guitar concerto. Beautiful!
I personally prefer anything involving Beethoven or Mozart, especially if it includes a glass harmonica.
if you can find a clean version of Adagio - Mozart, where it uses a glass harmonica rather than piano or flute, that's great.
Air on a G String
Vivaldi's Four Seasons
Since no one's mentioned him, anything by Gerald Finzi is really pretty. He's 20th century though.
debussy - clair de lune (used on the end of oceans 11)
disney fantasia soundtrack - waltz of the flowers,
grieg - morning from peer gynt
handel - largo from xerces
clint mansell and the kronos quartet - lux aeterna, summer overture (from the requiem for a dream soundtrack and used on many trailers)
lakme - leo delibes - flower duet (maria callas)
rossini - the thieving magpie, the barber of seville (my favourite! i love the bugs bunny cartoon the rabbit of seville too)
tchaikovsky - dance of the sugar plum fairy, pas de deux, march of the toy solders :) everyone knows this tune
thomas newman - plastic bag theme
yann tiersen - la valse d'amelie (piano or accordion version), comptine d'un autre ete: l'ap, les deux pianos,
tasmanian symphony orchestra - wild swans concert suite - eliza aria (that song from the advert with the cartoon people)
ludovico eunadi - fuori dal mondo
prokofiev - romeo and juliet op. 64:48 aubade
boccherini - minuet
chopin - nocturne
Yann Tiersen is not a classical performer / composer, so I doubt if classical is what you are looking for.
Moonlight Sonata- Beethoven
The 1st movement is the most popular, but the best part in my opinion is the 3rd movement..Simply because it sounds beautiful and it kind of hooks you to it..
Go to Google video and type in Wilhelm Kempff.. You'll find it there!
Air on the G String- J.S.Bach
This is also another amazing piece... It's just simply beautiful!
song from a secret garden? Are you referring to classical as describing the music or the era in which the music was written?
Have you heard about Vincenso Bellini? I recommend you to listen the part "Castadiva" from opera Norma of Bellini. It's one of the most beautiful masterpieces, 10 out of 10. It made me cry when i heard it for the first time. Extraordinary. Hope you think same as me.
The Godfather Soundtracks, their amazing