For me, this is the best season for anime OPs and EDs since spring 2009 (Pandora Hearts, Requiem for the Phantom, Shangri-la, etc.).
This season, we have Sakamichi no Apollon, Hyouka, Tasogare Otome x Amnesia, Jormungand, Hiiro no Kakera, Sankarea, Eureka 7 Ao, and Natsuiro Kiseki.
It's always hard for me to differentiate between the music and the images. I tend to base my preferences on the music, whether the animation is stellar or not.
Anyway, here are my favorites, with a bit of comment about each one. I'm not putting them in definite order, but I'll start with Sakamichi no Apollon's OP, "Sakamichi no Melody". It's a vivid marriage between Kanno Youko's music, and Yuki's lyrics and singing. Not really jazz. I even hear a bit of Beatles in there. But a great song. And the images and rhythms of the visuals work for me:
Next, here's "Yasashisa no Riyu", the OP to Hyouka, which is the first KyoAni show I've really liked since Clannad -- or even Haruhi. The voice of Choucho (the name means "butterfly") is entrancing and strong.
The images are wonderful, despite the fact that I don't think they made the raindrops-in-a-pool imagery they apparently love so much actually work, at least in the early part of the OP. The rhythms of it don't fit, for me. But that means little against the otherwise great KyoAni animation. I particularly like the amazing "girliness" of the way Eru runs into the clubroom, and the gust of wind blowing the friends' clothes as they stand together at the railing:
"Choir Jail" (whatever that means) is the OP to Tasogare Otome x Amnesia. Like the first two, this is also one of my favorite shows of the season. The sure and powerful voice of 15-year-old Suzuki Konomi is totally amazing, even if her interpretation can seem a bit coarse at times. The images from Silver Link are wonderful. I couldn't find an embeddable video of the actual OP online. This is a PV based on it, and with the image mirror-reversed:
The OP to Jormungand is Kawada Mami's "Borderland". The techno vibes and snappy imagery are perfect for this underappreciated show:
Fujita Maiko both wrote and sang the OP for Hiiro no Kakera, "Nee", and it's beautiful. Her leaps from low notes to high notes may be a bit awkward, but they are thrilling and emotionally moving, for me. The images are nothing special, but they work to introduce the show:
Sankarea's OP combines the rough pop of nano.RIPE with dream-like images from Studio DEEN that almost make me think of Shaft work:
For some reason, people do not seem that interested in Sphere's show, Natsuiro Kiseki, but I'm enjoying it. When their OP, "Non-stop Road" starts, I always think they are about to sing "Country Roads". But the song itself is good, and the images work beautifully to introduce the show. This is another video that has been mirror-reversed:
I am a big fan of the Kyushu all-girl rock band Stereopony, so even though this is not their best song, and the images are just okay, their ED for Eureka Seven AO, "Stand by Me," is definitely on my list. This video is also reversed:
Finally, here is the ED to Hyouka. "Madoromi no Yakusoku" is not the greatest song, although seiyuus Satou Satomi and Kayano Ai show they can do a nice job, for seiyuus. But the animation is godly. The movements of the girls are so soft and real. Just amazing. Some of the most libidinous animation I've ever seen:
EDIT: And there's more! As I think about it more, there are at least a couple more OPs I like. First, the OP to AKB0048, "Kibou ni Tsuite", by "NO NAME," which is a new sub-unit of AKB48, featuring the members who do voices in the anime. This is classic idol pop, but with some Kawamori feeling to it. And I love the big visuals, even the 3DCG that some other people hate:
And this next one isn't even a song, but it's an OP I always watch through: "A New Wuthering Heights", the OP to Lupin 3 - The Woman Known As Mine Fujiko. It's by Kikuchi Naruyoshi and Pepe Tormento Azucarar, with Hashimoto Ichiko. It may be Hashimoto speaking the words, although I have always thought it was Sawashiro Miyuki herself. The images are highly artistic and slightly NSFW: