Seconding Holst's 'The Planets'. Jupiter is my favorite out of the set.
https://www.youtube.com/watch?v=Nz0b4STz1lo

Modest Mussorgsky - "Pictures In an Exhibition"
https://www.youtube.com/watch?v=FsvpFU7KY7E

Ottorino Respighi - "The Pines of Rome"
https://www.youtube.com/watch?v=62V-ALlLZSg

Pyotr Ilyich Tchaikovsky - "Waltz of the Flowers" from "The Nutcracker"
https://www.youtube.com/watch?v=QxHkLdQy5f0

Franz Von Suppe - "Light Cavalry Overture"
https://www.youtube.com/watch?v=aF5nhMIyeqI

Edward Elgar - "Nimrod" Hands down my favorite Elgar piece.
https://www.youtube.com/watch?v=NhnMd1Jl7SA

I also love Opera! I've included recordings without vocals, since you may find them distracting.

Johann Strauss - "Ballet Music" from "Die Fledermaus"
https://www.youtube.com/watch?v=HzilaMovGJw

Giacomo Puccini - "Musetta's Waltz" from "La Boheme"
https://www.youtube.com/watch?v=KP3lV-YvCYM

And some Chinese orchestral/solo pieces. These works tend to be more descriptive or tell a story.

Chen Gang and He Zhanhao - "The Butterfly Lovers' Concerto" [A little information of the story of the piece.]
https://www.youtube.com/watch?v=DK3jRo6aTbQ

Yin Chengzong and Chu Wanghua - "Yellow River Piano Concerto"
Part 1, 'Song of the Yellow River Boatman' and 2 'Ode to the Yellow River': https://www.youtube.com/watch?v=zJBU9TyRA80
Part 3, 'The Yellow River in Wrath': https://www.youtube.com/watch?v=hc2ehaIbtAw
Part 4, 'Defend the Yellow River': https://www.youtube.com/watch?v=aw5EXroUN30

Ren Guang - "Colourful Clouds Chasing the Moon"
https://www.youtube.com/watch?v=V0GESu3Dg5c

Lü Wencheng - "Fisherman's Song At Dusk " This was my Dad's favorite song from his childhood. I managed to play it for him while I was learning violin a few years ago.
https://www.youtube.com/watch?v=N_45KQ_05Sk

And Joe Hisaishi has really good soundtrack pieces:

"Kaze no Torimichi" from My Neighbor Totoro
https://www.youtube.com/watch?v=vsi5ICLiZNA

"Merry Go Round of Life" from Howl's Moving Castle
https://www.youtube.com/watch?v=31nOaXSeqSo

The main theme from "Princess Mononoke"
https://www.youtube.com/watch?v=nBADF1LdP3g

personally not alot of these give me the motivation i need to get through a long night of studying, so ill post a couple personal favorite instrumental tunes
https://www.youtube.com/watch?v=_7dpgYO251M
https://www.youtube.com/watch?v=HDsQshrjIO0
https://www.youtube.com/watch?v=8d8LFBorTdw

I've seen a lot of orchestral classical music mentioned, so I'll suggest looking at solo piano and some concertos.

The essentials for solo piano:
Chopin ballade 1 - https://www.youtube.com/watch?v=RR7eUSFsn28
Beethoven Moonlight/Pathetique/Appasionata sonatas- https://www.youtube.com/watch?v=GXjhc8EbY4I
https://www.youtube.com/watch?v=a8XYrNrlBj4 https://www.youtube.com/watch?v=4C3TIr2bBo0
Mozart A minor sonata- https://www.youtube.com/watch?v=OWIEI9Qn_cA

Concertos:
Rachmaninoff 2/3 piano concertos- https://www.youtube.com/watch?v=EWgYg5Iicqk https://www.youtube.com/watch?v=MOOfoW5_2iE
Sibelius violin concerto- https://www.youtube.com/watch?v=ITTbY1n3Iz8
Mendelssohn violin concerto- https://www.youtube.com/watch?v=o1dBg__wsuo
Tchaikovsky violin concerto- https://www.youtube.com/watch?v=fKhZP3TdrA8
Dvorak cello concerto- https://www.youtube.com/watch?v=I002Aq1o3Pg
Elgar cello concerto- https://www.youtube.com/watch?v=ngcxp4yn_Fg

A lot of people find really high soprano annoying, but I love it. enjoy :)

https://www.youtube.com/watch?v=OLlux8ICOfI

https://www.youtube.com/user/UnsungMasterworks/videos

Lots of really nice stuff there, which you're unlikely to have ever heard before.

Bumping with some more music.

Lundgren's "Frösöblomster" is pretty cool, particularly in trombone quartet.
https://www.youtube.com/watch?v=K_MAJiEl1QA

The Mnozil Brass is a kickass group. Here's a few great performances of theirs:
William Tell Overture:
https://www.youtube.com/watch?v=uzpUaUIrabc
Florentiner March
https://www.youtube.com/watch?v=KxftY2-v1FM

Ravel's "Bolero" has some great atmosphere.
https://www.youtube.com/watch?v=3KgpEru9lhw

Joseph Alessi has a pretty great performance of "Blue Bells of Scotland"
https://www.youtube.com/watch?v=YH6lcElZr-k

Same goes for Winston Marsalis playing "Carnival of Venice"
https://www.youtube.com/watch?v=inED9IicIpc

and ill end this post with a bit of jazz. Maynard Ferguson playing "Birdland"
https://www.youtube.com/watch?v=idGvKFbYgI4

EDIT: Actually, wanted to put up some 8-Bit Style as well.
Kubbi - Up in My Jam(All of a sudden)
https://www.youtube.com/watch?v=8YXPucedPzs

Mega Man 2 Soundtrack
https://www.youtube.com/watch?v=BnFs2J8c-kU

Crypt of the Necrodancer Soundtrack (Great game too)
https://www.youtube.com/watch?v=UrS1RyuoG0I

When you say "instrumental" do you mean any kind of music without lyrics or specifically ambient music that doesn't have much of a beat/rhythm whatsoever?

btw, if you have to write something and don't want to be distracted, download OmmWriter. Complete removes all distractions, plays some meditation music and lets you concentrate fully on your writing.

I put together a wide selection, all of these don't have lyrics and have a slow/relaxing rhythm, although they are from different genres. (can't post youtube links right now though due to internet censorship here). Sorry for the long post:

Classical/Neoclassical
Maxence Cyrin - The Fantasist
Tim Hecker - Dropped Pianos
Nils Frahm - The Bells
Nils Frahm - Felt
Nils Frahm - Spaces
Eric Satie - Gymnopedie
A Winged Victory for the Sullen - selftitled
Goldmund - The Malady of Elegance
Henryk Gorecki - Symphony No. 3 (Symphony of Sorrowful Songs) (maybe)

Ambient (nearly no rhythm)
Brian Eno - Ambient 1: Music for Airports
Brian Eno - Ambient 2: Plateaux of Mirror
Brian Eno - Ambient 3: Day of Radiance
Brian Eno - Ambient 4: On Land
Robert Rich - Somnium (maybe, originally a concept album to be played while sleeping, 7 hours long)
Michael Oster - Sound of a Dying Hurricane (field recording of a hurricane)
Chris Watson - Stepping into the Dark (Field recordings of a river at different times of the day)
Lawrence English - Kiri No Oto (ambient drone, not everyones taste)

Post-Rock
Orange Crush - Autumn Reflections
Godspeed You! Black Emperor - F# A#
Godspeed You! Black Emperor - Lift your skinny fists like antennas to heaven
Library Tapes - A Summer beneath the trees

Hip-Hop
Nujabes - Departure (maybe)
Nujabes - Metaphorical Music
Nujabes - Modal Soul
Nujabes - Spiritual State
Task the Samara - Flood (maybe)
Shigeto - Lineage
Blazo - Colours of Jazz (Jazz-Hop)
Athmosphere - Seven Travels Instrumentals (Maybe)
Clams Casino - Instrumentals
Edamame - Greenhouse (Instrumental Hip-Hop based on nature samples)
Kenishiro Nishihara - First Impressions
Kondor - Peace Of Soul

General Instrumental (different genres)
Aidan Clare - Home
The Album Leaf - In a Safe Place
Asa & Stumbleine - Your Secret
Austin Wintory - Journey
Ben Jordan - Pale Blue Dot
Bonobo - Black Sands
Bonobo - The North Borders
Burial - Kindred EP / Untrue / selftitled (Maybe)
Carbon Based Lifeforms - Interloper / TwentyThree (Maybe, don't really like them)
The Caretaker - An empty bliss beyond this world
Celer - Engaged Touches
David Lange - Return of the Comet
Dolphins into the Future - On Sea-Faring Isolation
Francis Harris - Leland (maybe)
From the Mouth of the Sun - Woven Tide
Hakobune - The Cowboy across the River
Helios - Unomia
Indignu - Odyssea (maybe)
Mark Lyrell - Tetrachromacy EP
Olafur Arnalds & Nils Frahm - Stare
One Thousand Lucky Cranes - selftitled
Portico Quartet - Isla
Portico Quartet - Knee-deep in the North Sea
Portico Quartet - selftitled
Pregnant Head - Afterlove (maybe)
Pregnant Head - Disintegration (maybe)
Robert Farrugia - They Glistened Sharply Through Morning Dew
Naono - Sleepy Pebbles
SBTRKT - selftitled
Sigmund Freund - Experiri
Sigmund Freund - Kallang Bahru
Soma - kata2 (maybe)
Takitani - Songs 1
Western Jupiter - Arimillaria EP
Woob - Woob² 4495 (maybe)

This guy knows what's up. B)
I'd also add in Adam's Lament by Arvo Pärt, one of his latest masterpieces.

https://www.youtube.com/watch?v=SuOAL3mGzNc

.

Rachel's is really nice relaxing instrumental music.

https://www.youtube.com/watch?v=xeCnE2LQZik

Enigma Variations - Elgar:
https://www.youtube.com/watch?v=VMLnoe957Ls

Planets - Holst:
https://www.youtube.com/watch?v=AHVsszW7Nds

First Suite in E flat - Holst:
https://www.youtube.com/watch?v=fLbP6qpI1YI

Gymnopedie no. 1 - Satie:
https://www.youtube.com/watch?v=S-Xm7s9eGxU

Soundtracks:
Skyrim:
https://www.youtube.com/watch?v=aQeIYVM3YBM

Oblivion:
https://www.youtube.com/watch?v=SpqSdORmCX4

Morrowind:
https://www.youtube.com/watch?v=xULTMMgwLuo

Bastion:
https://www.youtube.com/watch?v=oLA0vB9LCTM

I nearly got carpal tunnel playing snare for that, but great recommendation.

I've been listening to this will destroy you, boards of canada and explosions in the sky for studying mostly. Good stuff

Ksshiwa Daisuke - Rabbit's Quartet

Aphex Twin is p good too
https://www.youtube.com/watch?v=Q0q1gCsZykg
https://www.youtube.com/watch?v=RhHkUg-QCwk
https://www.youtube.com/watch?v=PeLuQ6X2ixI
https://www.youtube.com/watch?v=gOKHfOQ8-xY

http://open.spotify.com/user/mynameislinea/playlist/5Fq64a52kow0iivojKlad0 has everything you'll ever need ever(like 8k songs/good leads), it's been running every day for me for a couple months and I'm still hearing new tracks

no one has mentioned william basinski's work, check out his body of work. 'the disintegration loops' is probably his most popular collection.

piggybacking off cloudmaker aphex twin is pretty much the greatest electronic musician of all time so do check out his discography
the above link has selected ambient works 2, but also see if you can score a dl of SAW 85-92, melodies from mars, i care because you do, the richard d. james album and drukqs for less acidy more melodic and ambient pieces by him, it all comes highly recommended

also if you can find any valium aggelein they're worth listening to. same goes for sun araw. burzum is also pretty dope if you're into that sort of thing(I started with filosofem)

el ten eleven is a great instrumental band.

https://www.youtube.com/watch?v=DfM46XR8wGQ

Buckethead somehow slipped my mind, but here ya go - all instrumental, but not classical.
Lone Sal Bug
I love my parents
Sail on Soothsayer

Here are my favorite classical pieces:
Saint-Saens: Introduction et Rondo Capriccioso
https://www.youtube.com/watch?v=-HQyXWkABo0

My favorite version of the Sibelius Violin Concerto
https://www.youtube.com/watch?v=YsbrRAgv1b4

Sarasate: Zigeunerweisen
https://www.youtube.com/watch?v=xir-5oAWxXE

Sarasate: Carmen Fantasy
https://www.youtube.com/watch?v=FIaOyur3Qcw

Paganini: La Campanella
https://www.youtube.com/watch?v=YaxHZxvmSwQ

Paganini: Violin Caprices No. 1, 5, and 24
https://www.youtube.com/watch?v=uCePRgqO-HI
My preferred version of 24:
https://www.youtube.com/watch?v=vPcnGrie__M

Paganini: Moto Perpetuo
https://www.youtube.com/watch?v=dPRWshWq9E4

Dinicu: Hora Staccato(arranged by Heifetz)
https://www.youtube.com/watch?v=Mag2mc5Vva0

Liszt: Hungarian Rhapsody No. 2
https://www.youtube.com/watch?v=7H99FM6S8rU

Bach: Double Violin Concerto
https://www.youtube.com/watch?v=DJh6i-t_I1Q

F.Kreisler - Sicilienne & Rigaudon (Rigaudon starts 1:50)
https://www.youtube.com/watch?v=-7m373HqFfk

Antonin Dvorak - New World Symphony
https://www.youtube.com/watch?v=ETNoPqYAIPI

Tchaikovsky - 1812 Overture
https://www.youtube.com/watch?v=VbxgYlcNxE8

Handel Halvorsen - Passacaglia
https://www.youtube.com/watch?v=dZawzc8HJio

Vivaldi - four seasons (all four of them)
https://www.youtube.com/watch?v=GRxofEmo3HA

Vivaldi - la folia
https://www.youtube.com/watch?v=9BLfaQ98FbM

Mozart - Symphony 40 in G minor (3rd movement)
https://www.youtube.com/watch?v=NjR2_BQAHTs

Most if not all of these were mentioned already but holy shit The Planets Suite by Holst is so fucking good. Vivaldi is a pretty cool guy as well.

Mozart's 4th horn concerto is amazing, especially the rondo.
4th horn concerto

Fanfare for the common man simple and incredible
Fanfare for the common man

The entirety of the new world symphony is also incredible but damn the build up at 32:15 into the hit at 32:24 gives me freaking chills.
A new world symphony

I may be a bit biased as I played that last piece in highschool marching band and the horn concerto was my audition piece for college.