This could get long, lol...so many great themes in my opinion.
Track name - Artist - Series
(all artist names are surname/given name order where applicable)
Howling - abingdon boys school - Darker than Black
Kesenai Tsumi - Kitade Nana - Full Metal Alchemist
Higurashi no Naku Koro ni - Shimamiya Eiko -
Uragiri no Yuuyake - Theater Brook - Durarara
Tank! - Kanno Yoko and the Seatbelts - Cowboy Bebop
Rain (Ballad of a Fallen Angel) - Kanno Yoko - Cowboy Bebop
Tokihanate! - Houko Kuwashima- Blue Gender
Lilium (Lily) - Kondo Yukio - Elfen Leid
Duvet - Bôa (vocals: Jasmine Rodgers) - Serial Experiments Lain
*~Asterisk~ - ORANGE RANGE - Bleach (1st OP)
Life is Like a Boat - Fu Rie - Bleach (1st ED)
Rolling Star - YUI - Bleach (5th OP)
the WORLD - Nightmare - Death Note
Crossing Field - LiSA - Sword Art Online (1st OP)
Overfly - Haruna Luna - Sword Art Online (2nd ED)
Ride on Shooting Star - the pillows - FLCL
Motteke! Sailor Fuku - Hirano Aya, Kato Emiri, Fukuhara Kaori, and Endo Aya - Lucky Star
I have others, but these are on their own playlist cuz I listen to them sooooooo much. Some I like for the darker tone, some for the upbeat, and others...well, because I relate to stuff like "And you don't seem to understand..." (Duvet) "Nobody knows who I really am..." (Life if Like a Boat) being so misunderstood by so many, which makes me "walk in the rain." Then there's Lilium...such an IRONY to end on "O Castitas Lilium" (Oh pure Lily) when talking about Lucy.
And although I don't know the title, the opening theme from Crest/Banner of the Stars tends to stick in my head despite being instrumental.