the best, nicest classical music?

There is no "best" or "nicest" classical music.

One of my favorite compositions are the Goldberg Variations by J. S. Bach.

Try the version of Glen Gould:

http://www.youtube.com/watch?v=g7LWANJFHEs

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.

The Canon by Pachelbel.

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!

http://uk.youtube.com/watch?v=7VGQ8Jkplrw&feature=related http://uk.youtube.com/watch?v=e4P1FpRwgBU this is some I enjoy hope you enjoy them too

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.

Canon in D

A lot of the Death Note(anime) soundtrack is classical and also very beautiful.

I love Lilium by Kumiko Noma as well - http://uk.youtube.com/watch?v=wsR8tY2psmw&feature=channel_page

Also as someone else mentioned, Lux Aeterna by Clint mansell is amazing - http://uk.youtube.com/watch?v=hKLpJtvzlEI&feature=channel_page

The Godfather Soundtracks, their amazing