Full Moon wo Sagashite has a fantastic selection...And...I ADORE the opening!! It's so cute!! Also, I really like "Angelus" from InuYasha. DANCE SONG! XD Seriously, that song makes me want to dance! Anyways, I have an attachment to Every Heart (InuYasha), too...It was the ending theme that played during my first months of watching the show...Ah, memories!
I love the (4th?) ending theme for Rurouni Kenshin, too...4th Ave. Cafe! Sooo catchy! Also, Yuzurenai Negai, from Magic Knight Rayearth...LOVE it! What else...Well, I couldn't possibly leave out Tank! and The Real Folk Blues, from Bebop. And I also love Words that We Couldn't Say, even though it's not literally a theme song. Ready, Steady, GO! and Rewrite are two more favorites from FullMetal Alchemist, and Ride on Shooting Star, from FLCL, is an awesome one, too. Oooh...And Loosey, from Bakuretsu Tenshi! It's odd that I like that song, because it's sort of like J-rap(and I hate rap with a passion, haha), but then again, it's really jazzy, and SUPER catchy. I hate the anime it's from, though. XD
Oh, and uh...Kaze wa Mirai ni Fuku, from Trigun. I don't know how...it grew on me. ...Stop giving me weird looks.