I wrote OPs a bit earlier and the ranking hasn't changed so...
and ugh everything is blocked on Youtube
1. Sakamichi no Apollon-- Sakamichi no Melody
This song is just so sick, with the powerful instruments in the background as it changes tempo. It feels like actual music as opposed to generic pop that a lot of anime is prone to. Or annoying whiny/chipmunk stuff. But you'd expect no less from Yoko Kanno. What really helps is the scenes that the music accompanies, capturing the show's essence in a minute in a half. I can't get enough of it, I'd say.
2. Fate/Zero-- To the Beginning
The first OP to Fate/Zero was alright but a bit on the weak side. Lisa sang alright for Angel Beats and Oath Sign but I always felt her voice was too weak. The 2nd OP just feels more powerful and suited to an epic story like Fate/Zero. The visuals tease us to what has happened and what will happen. Sliding down the finish line; that's what it felt like.
3. Shakugan no Shana III- Serment
While the first half of Shana's last season was cursed with mediocre sounds and certainly NOT Kotoko's best work, they kicked off the last half with a song in 2012 that really reminds me of some last stage in a video game. The fact that Mami Kawada's back to sing it and it keeps reflecting past nostalgic memories in its scenes really helps drives the point home of FINAL. Questionable writing outside, great OP.
Honorable Mention: Nisemonogatari-- Futakotome for sounding a continuation of "Staple Staple"
ED-- I usually don't care for EDs:
1.) Shin Sekai Yori ED
I don't know. I just found it insanely catchy, and fits the delirium of the series really well. The visuals also go along well; what with the descent into something extremely unsettling
2.)
Psychopass ED1- It sounds very powerful despite the relatively quiet vocals that start out the song. Instruments kick ass throughout. A mix of somberness into something of high energy-- kinda dark. Kinda like the show itself The most notable thing about this is that it's really cool, and is reminiscent of Ghost in the Shell.
3.)
Rinne no Lagrange-- Hello
Nice and relaxing. Sadly the series was like that too, and I fell asleep. Still the bells are just so well done.
Honorable Mention: Fate/Zero ED2
Tari Tari-- Kokoro no Senritsu (But this is a special ED, so I am cheating)