For myself, the best part of anime is usually the songs. And in no particular order, here are some that I like.

Rurouni Kenshin - Opening 1 - Sobakasu: https://www.youtube.com/watch?v=0bxNEtkGG7U
Rurouni Kenshin - Opening 2 - 1/2: https://www.youtube.com/watch?v=RK4lN7pr8C8
Elfen Lied - Opening - Lilium: https://www.youtube.com/watch?v=Q78bn1ubP9o
Angel Beats - Opening - My Soul, Your Beats: https://www.youtube.com/watch?v=zIFV8UUs1-c
.hack//Sign - Opening - Obsession: https://soundcloud.com/justforgivemethistime/obsession-see-saw

Here's my youtube playlist: https://www.youtube.com/playlist?list=PLofMFQZ4Tec4MaHBsG_zNl5jKr9uPWjtT

Unfortunately quite a few of them aren't allowed to be played anymore. Fixed a few of them.

What are some that you guys like?

 

Konya wa Hurricane - Bubblegum Crisis: https://www.youtube.com/watch?v=ajTAnMqhZB8
Mad Machine - Bubblegum Crisis: https://www.youtube.com/watch?v=zVq7WoflC6k
Prism - Gokudo: https://youtu.be/h-0rm62rRhk
Flying in the Sky - G Gundam: https://youtu.be/FK9Y_8GN2h0
The Hero - One Punch Man: https://youtu.be/QImBolnTVH8
Hikaru nara - Your Lie in April: https://youtu.be/3bm8vZVFYyU
H.T. - Trigun: https://youtu.be/m_nVgFoeDmc
Last Dinosaur - FLCL: https://youtu.be/oYzQ5QqVD-M
Little Busters - FLCL: https://youtu.be/cu1yijNTeus

I'll think of more later.

 

Guilty Crown, Full Metal Alchemist: Brotherhood, Samurai Champloo (Nujabes!) all have pretty great openings in my opinion, but my favourite is definitely Baccano's.

The only ED I can think of is Naruto's Wind by Akeboshi.

 

Shadow Skill - Opening - Born Legend: https://www.youtube.com/watch?v=sDc-wjzdle4
Vandread - Opening - Trust: https://www.youtube.com/watch?v=kN9TD_Txy2k
Paranoia Agent - Opening - Dream Island Obsessional Park: https://www.youtube.com/watch?v=-anabfAg06U
Ergo Proxy - Opening - Kiri: https://www.youtube.com/watch?v=oAXrRWLKzko
Baccano - Opening - Guns & Roses: https://www.youtube.com/watch?v=Msg8ypnLqaw

Heh.

 

I quite like the OP from Fate/Stay Night: Unlimited Blade Works' second season

 

I think I attributed the right artists. Full versions of the songs can probably be found easily enough if you want, but I linked the openings/endings themselves here.

Spoiler

A Cruel Angel’s Thesis, by Yoko Takahashi - Neon Genesis Evangelion

Battlecry, by Nujabes - Samurai Champloo

Brave Shine, by Aimer - Fate/Stay Night: Unlimited Blade Works

Duvet, by Boa - Serial Experiments Lain

Fly Me to the Moon, by Claire Littley - Neon Genesis Evangelion

Hitomi no Tsubasa, by Access - Code Geass: Lelouch of the Rebellion

Ideal White, by Mashiro Ayano - Fate/Stay Night: Unlimited Blade Works

Inner Universe, by Origa - Ghost in the Shell: Stand Alone Complex

Kiri, by Monoral - Ergo Proxy

Magia, by Kalafina - Puella Magi Madoka Magica

O2, by Orange Range - Code Geass: Lelouch of the Rebellion

Oath Sign, by LiSA - Fate/Zero

Rise, by Origa - Ghost in the Shell: Stand Alone Complex

Shiki no Uta, by Minmi - Samurai Champloo

Tank!, by The Seatbelts - Cowboy Bebop

The Hero, by Jam Project - One Punch Man

The Real Folk Blues, by The Seatbelts - Cowboy Bebop

The World Without Logos, by Yasushi Ishii - Hellsing

To the Beginning, by Kalafina - Fate/Zero

The rest here is some music I like from anime in general that I felt I needed to include.

Spoiler

Blue, by The Seatbelts - Cowboy Bebop

Chant I: Making of Cyborg, by Kenji Kawai - Ghost in the Shell

Decretum, by Yuki Kajiura - Puella Magi Madoka Magica

Gotta Knock A Little Harder, by The Seatbelts - Cowboy Bebop

Komm, Süsser Tod, by Arianne - The End of Evangelion

Point Zero, by Yuki Kajiura - Fate/Zero

Rain, by The Seatbelts - Cowboy Bebop

Sis Puella Magica! / Fateful #1, by Yuki Kajiura - Puella Magi Madoka Magica

Thanatos / Substitute Invasion, by Shiro Sagisu - The End of Evangelion

Thanatos (If I Can’t Be Yours), by Loren & Mash - The End of Evangelion

The Ballad of Puppets: Flowers Grieve and Fall, by Kenji Kawai - Ghost in the Shell 2: Innocence

The Battle is to the Strong, by Yuki Kajiura - Fate/Zero

The Beast II / Sin From Genesis, by Shiro Sagisu - Neon Genesis Evangelion

The Cyborg Fights, by Makoto Miyazaki - One Punch Man

The Flow of Emptiness, by Shiro Sagisu - The End of Evangelion

Theme of One Punch Man, by Makoto Miyazaki - One Punch Man

 

I find your political opinions to be questionable at best, but I must say, you have excellent taste in music. I don't listen to much anime music at all, but you have a lot of what I do on this list!

 

I concur with all the recs for OPM soundtracks, but feel like the closing theme should not be left out. I was very surprised when I first heard it, considering it's the exact opposite of The Hero, the opening theme, but it's amazing. Very calm, and one of the few anime songs whose lyrics actually work rather well.

Others include:
The first season opening of Sword Art Online, which is Crossing Field by LiSA

Nandemonaiya by Randwimps for the movie Kimi No Na Wa. (Your Name)

The English version of the Shaman King opening will always hold a special place in my heart, one of the few anime that played in television when I was very, very young. Hypes me up even now.

Speaking of stuff from my childhood, have some Yu-Gi-Oh and some Pokemon because they deserve mentions for sheer nostalgia.

I know it's not an opening or closing song, but Lost My Pieces from Toradora, worked incredibly well with its scene and even on its own is a great piece of music.

For something more mainstream, the openings from the first and second seasons of One Piece. Heh, the second one inspired me to write a fic, once. Good times.

On the Naruto side of the mainstream, we have Naruto opening 9, Yura Yura by Hearts Grow.
Naruto Shippuuden opening 3 'Blue Bird' , 6 'Sign' by Flow and 7, "Toumei Datta Sekai" by Motohiro Hata

 

Nostalgia aye?

Digimon Frontier - Opening - A World For Us All: https://www.youtube.com/watch?v=9eOJsm9ubGk
Beyblade - Opening - Let's Beyblade: https://www.youtube.com/watch?v=N74cnBa_Bmc
Medabots - Opening - Medabots Opening: https://www.youtube.com/watch?v=alOdQsdPCkg

Technically doesn't count if you're very rigid about what anime is, but it's nostalgic.

W.I.T.C.H. - Opening - We Are W.I.T.C.H.: https://www.youtube.com/watch?v=ldyraUyiU-A

 

You can't post Digimon and not post Butterfly from the original Digimon and The Biggest Dreamer from Tamers.

Similarly, if we're talking classic shounen openings you can't go wrong with Naruto's very first one, ROCKS or Fighting Dreamers, and for Bleach there's the first one that are unforgettable.

Outside of shonen, there's Gundam. The original is iconic, 8th MS team and Men of Destiny from Stardust Memory are just good songs/openings that the shows didn't really live up to, I fucking love From the Aqueous Star With Love... Going away from UC, there's also Just Communication and Rhythm Emotion.

 

I have too many to list, since I really enjoy listening to anime openings and endings too, but here are some of my favorites off the top of my head:

Kannazuki no Miko ending - Agony by KOTOKO
Shuffle! opening - YOU
Soul Eater opening - Resonance
Naruto Shippuuden ending - Freedom
Bleach opening - Scandal by Shoujo S
Rozen Maiden opening - Kinjirareta Asobi
Kanon opening - Last regrets (might as well mention Air opening)

Makes me wish I had a proper list somewhere.

I also really like the Fate, Angel Beats and Elfen Lied songs already mentioned.

 

Big fan of virtually all Bleach OPs, 1,2,10 particularly, I think its one of the reasons I could stomach 350 episodes of that shit.

ShinSekai Yori's ED is incredible

Also a huge fan of FMA/FMA:B OP/ED's, with Rewrite from the original and Golden Time Lover from Brotherhood being the absolute best, imo.

EDIT: also my god YUI's voice in Bleach OP5. I would do dirty things to her voice.

 

Shows like Bleach and Naruto really don't do it for me, but back when I watched it on Toonami there actually was one Bleach opening I liked.

EDIT: While I'm at it, these K-On! endings [1, 2] were good too.

 

To be honest, I preferred Folder 5's other song.

One Piece - Jango's Dance Carnival - Ready: https://youtu.be/dYt4gtbfi1o?t=2m36s

 

Bleach OP 2 - it reminds me of how Bleach used to feel when it was actually good
Gundam SEED Destiny OP 3 - Bokutachi no Yukue - the anime was a mess, but the OP is super catchy and has a really nice beat
Rahxephon - beautifully surrealist and really captures the essence of the show without giving much away
Ghost in the Shell SAC - a fantastic job of catching the almost spiritualist, which still post-modern feel of the show. Not a huge fan of the 3D animation though
Ghost in the Shell SAC 2nd Gig - not nearly as spiritualist as the previous one but still very good. And no 3D animation!
Eden of the East - A classic. The abuse of greatness is when it disjoins remorse from power

Those are the ones which come to mind without much thinking about it.

 

Lol what the fuck was that

 

Me mixing up Ready and Believe it seems.

 

Rin: Daughters of Mnemosyne OP/ED

To date, probably my favorite OP/ED, though I'll admit I'm not a huge consumer.

 

Here are some of my favorites:
Baby Steps OP 2 (Believe in Yourself - Mao Abe)
Erased OP (Re:Re: - Asian Kung Fu Generation)
Little Busters OP
Little Busters Refrain OP
Kono Suba OP 1
Yu-Gi-Oh! OP 5 OVERLAP - KIMERU
Steins;Gate OP Hacking to the Gate - Itou Kanako
Ga-Rei Zero OP
Supernatural: The Animation ED
Death Note OP 1
Code Geass Opening 1
Naruto OP 2 Haruka Kanata
Naruto Shippuden opening 2 You Are My Friend
Naruto Shippuden Opening 6 "Sign" by FLOW
Naruto Shippuden Opening 7 "Toumei Datta Sekai" by Motohiro Hata
Naruto Shippuuden OP 11
Kuromukuro OP 1
Mobile Suit Gundam Iron Blooded Orphans OP 1 Raise Your Flag
Attack on Titan OP 1