Hmm, I want to play. I'll give you a sampling of a dozen of each type, starting with anime songs.
I've included (youtube) links to some of the songs that I especially want to share, since they might not be familiar to a lot of people. I listened to a lot of these songs again in order to compile these lists, a project which had two effects: 1) making me appreciate everything all over again, and 2) making me feel old. Oh well.
Anison
- Geki! Teikoku Kageki-dan - Yokoyama Chisa et al., the "Hana-gumi" (Sakura Taisen OP)
- Give a Reason - Hayashibara Megumi (Slayers Next OP)
- Allegro Cantabile - Suemitsu & the Suemith (Nodame Cantabile OP)
- Pure Snow - Sasaki Yuuko (Himiko-den OP)
- Melissa - Porno Graffitti (Fullmetal Alchemist OP1)
- Saikyou Pare Parade - Hirano Aya, Chihara Minori, Gotou Yuuko (Haruhi radio show OP... okay, not really an anime song; whatever)
- Sore ga, ai deshou - Shimokawa Mikuni (Full Metal Panic! Fumoffu? OP)
- Hishoku no Sora - Kawada Mami (Shakugan no Shana OP1) (Should you disapprove of the way I vote, you can pretty much blame this song; this is how it all started.)
- The Light Before We Land - The Delgados (Gunslinger Girl OP)
- Mysterious Eyes - Garnet Crow (Meitantei Conan OP7) (Garnet Crow has a strange composition: a vocalist, a guitarist, and two keyboardists. I'd say that Nakamura Yuri's charmingly low, slightly husky voice is the key to the band's sound.)
- Call Me, Call Me - Steve Conte (Cowboy Bebop)
- Blue - Yamane Mai (Cowboy Bebop) (If this song consisted only of the parts where she belts out the word "free," it would still be amazing. No black and white in the blue.)
Honorable mention, showing my age:
- Boku de aru tame ni - Flying Kids (You're Under Arrest OP1)
- 13-gatsu no Kakumei - Fence of Defense (El Hazard: the Alternative World OP)
J-pop
- Ooki na Tsubasa - Yano Maki (I remember Ooki na Tsubasa as the gateway song, so it stands a cut above everything else. I have a feeling that if this were strictly a list of my favorite J-pop, Yano Maki songs would take up half the spaces.)
- Ai no tame ni - Ueto Aya
- come again - m-flo
- miss you - m-flo loves melody. & Yamamoto Ryouhei
- Tenohira, Kurumi - Mr. Children (Two songs, but they're on the same single, so cut me some slack here.)
- Omoi no mama ni - Nakanomori Band
- Fuuka Fuusou - Cocco (「悲しみ愛より深い」のはだあれ? This song has simple yet stunning lyrics. There used to be an excellent translation somewhere, but I can't find it anymore.)
- Hikari - Utada Hikaru (If Yano Maki takes up one half, Hikki might speak for the other half.)
- Utakata - YeLLOW Generation
- Niji - Fukuyama Masaharu (ED to Waterboys, not that I've ever watched it.)
- Yuki no Hana - Nakashima Mika
- Kiseki - Uemura Kana (I doubt most J-pop fans have even heard of her, which is a shame. Her voice, and this song, had me from the first listen.)
Those are actually just lists of my favorite anime/J-pop songs not sung by
Sakamoto Maaya, my favorite Japanese artist thanks in no small part to her body of work with Kanno Youko, and owner of one of the purest singing voices I've ever heard. So, the next list:
Sakamoto Maaya
- Daniel (23-ji no Ongaku)
- Toto (23-ji no Ongaku)
- Vector (Escaflowne Movie Insert)
- Yubiwa (Escaflowne Movie ED)
- Yakusoku wa Iranai (Escaflowne OP) (As a sixteen-year-old, she not only sang the OP for Escaflowne, but also provided the voice of its heroine, Kanzaki Hitomi.)
- Mameshiba (Earth Girl Arjuna OP) (Truth is, I adore this song. I try not to play favorites too much when it comes to Maaya, but this one lights up my face to the same extent that "Daniel" gives me chills.)
- Tune the Rainbow (RahXephon Movie ED)
- Purachina/Platinum (Cardcaptor Sakura OP3)
- Scrap ~ Wakare no Uta (Shounen Alice) (愛と希望の物語り。。。)
- Yoru (Shounen Alice)
- Koucha (Lucy)
- Birds (Easy Listening)
And, lastly, the catch-all category for English-language music:
English
- Call and Answer - Barenaked Ladies
- The Old Apartment - Barenaked Ladies
- The Ground Beneath Her Feet - U2
- Every Little Thing She Does is Magic - The Police
- Leaving Town - Dexter Freebish
- Gravity - Vienna Teng (I saw her perform this live when I was in college; we're both alumni of the same university. Now she's famous and I'm... here.)
- Anna Begins - Counting Crows
- Barely Breathing - Duncan Sheik
- Auf Achse - Franz Ferdinand
- Creep - Radiohead
- Sackcloth and Ashes - The Mr. T Experience
- Hold Your Colour - Pendulum
What's up with that last list? It makes me sound like I'm sixteen.
I guess I'd say that I generally like songs with vibrant, memorable melodies. Strong vocals go a long way toward that--for some reason I'm partial to female vocalists in Japanese and male vocalists in English, though I've made the odd exception. I'd also venture that I have a natural affinity for any song that features violins.
If I were to compile a fifth list, it'd be instrumental stuff: probably a mishmash of video game music and classical music. This post is seriously tl;dr already, though, and I need to stop editing it.