I must start with this two pieces

1) Beethoven - Violin Concerto in D major

Truly masterpiece, also one of the greatest strings legato (just listen at 2:00).
I prefer perfomance with Isabelle Faust, but I can't find it on youtube

http://www.youtube.com/watch?v=CMP2fPT6cJA

2) Mahler - Symphony no.5

Another masterpiece and another best strings I ever hear in classical music (listen first part at 3:30).
I prefer Bernstain performance with Wienner PH. There is a lot of perfomances and it's really hard to find the right one.
On my PC I have four perfomances and I can't decide which one is better.

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

3) Mendelssohn - Symphonie Nr.4

Third in the list, but this list is with no order really I must admit.
Just wonderfull ! Flawless music.

http://www.youtube.com/watch?v=_HX_jF1_Tgc

4) Schubert - Symphony no. 9 (The greatest)

Nice staccato and legato lines... One of the best pieces with nice transformation from fff to ppp and vice versa

http://www.youtube.com/watch?v=kNocKxKd8-I

 

Beethoven has always been the more human of some of the most famous composers to me. Enjoy Piano Sonata No. 14:

http://www.youtube.com/watch?v=4Tr0otuiQuU

 

Shame they had no sub bass back in them days lol

 

There is so much to recommend, so I will limit myself to three pieces from three composers played by string quartets.
In order of achievement (I know it's a bold statement, but it's my humble opinion) :

Franz Schubert String Quartet D 804 "Rosamunde" by the Quartetto Italiano

Beethoven String Quartet Op.132 by the Quartetto Italiano

And last but not least, the masterpiece : J. S. Bach - Contrapunctus XIV by the Emerson String Quartet

 

anything by J.S, He wrote it all in some form before anyone else got the chance
but as you said classical, I imagine you mean the classical period, so as above but with a name swap for Mozart.
Important music ? usually means that it adds something different (new) like stravinsky did with fourths and rhythm for example
I like olivier messiaen, but I couldn't highlite a single piece, as I like his sound and his approach to composition, its both important and quality but classic rather than classical. I Wonder if Zappa will ever get the recognition deserved for his work, he's a quality composer but seems over looked for his contribution in the orchestral field.
here's some other guys who I like Panufnik, Ives
and some neoclassicists Poulenc, Hindemith and some Respighi

 

Mass in B Minor by J.S Bach.

(Sorry, I can`t get the video to show like you guys did. What am I doing wrong?)

 

just remove "s" in https

http://www.youtube.com/watch?v=7F7TVM8m95Y&gl

Vivaldi - Four Sessions

One more truly masterpiece !
All string articulations are included in this masterpiece, complete music theory


http://www.youtube.com/watch?v=yGcwvd0yaxM

Haydn - Symphony no 35

Genious who has most influence on another genius known as Mozart !

http://www.youtube.com/watch?v=LGpRas327uw

W.A.Mozart - Symphony no. 40

Everything say on this would be just empty word's.

http://www.youtube.com/watch?v=2HbMzu1aQW8

Shame, with all the orchestral libraries (terabites) we can't make anything like this !
Every try of remaking mockup on Mozart no. 40 (first staccatos) are waste of time, it's just impossible without true instruments and true musicians with feelings.

And then, just look at the today library cd's, every day minimal five libraries are available:

* dub this
* dub that
* club this
* club that

(just wondering who need all that stuff !???)

Shame, today's music are just loose that something, and that feeling

Just imagine this: those genious are compose this pieces from head and without a MIDI editor ! or even compressor

 

Can't agree more *yes*

People back in the days (way back, actually) were focused on their art, they didn't have so much distractions... internet being the most.
The liberalism, which leads to consumerism, is fucking us all up. Still, we are free to live in a different way, but who does ? and who cares ?

 

You should go to a real classical concert, then you'll listen to real subbass acoustically mixed thanks to very clever composition.