I don't watch much anime, almost no anime at all. Alot of the shows aired in the United States are...well...overrated. xD [*cough* Naruto. *cough*] And I use to majority of my free time to music instead of anime. But nonetheless...

All the openings and endings of the NANA series are awesome. <3

Openings:

Round Table ft. Nino - Let Me Be With You [Chobits' Opening]

It's groovy and cute. ^_~ The vocals are quite high-pitched, but controlled and soft.

Shing02 - Battlecry [Samurai Champloo opening]

I'm not a fan of hip-hop but anything with Shing02 is awesome.

L'arc~en~Ciel - Blurry Eyes [DNA2 opening]

It's L'arc~en~Ciel, so it's obviously wonderful. =3 I remember watching this anime long ago. I was young back then...watching a perverted anime. xD

--

Endings:

Suki Dakara [Bokura ga Ita ending]

Ningyo Hime [Chobits second ending]

THE BEST ENDING EVVEEEEEEEEEEER:


Minmi - Who's Theme [Samurai Champloo Ending]

Love it, marry it. xD It's so lovely! The relaxing atmosphere, the controlled vocals...AH! I can't explain! I wanna marry Minmi. I find it to be a inspiring song, with a melancholy feeling.

I got more! woohoo!

Days by FLOW -Eureka 7 opening
Himitsu Kichi by Takada Kozue -Eureka 7 ending
UNLIMITED by Aikawa Nanase -Samurai 7 opening
Fuhen by RIN -Samurai 7 ending
INVOKE by T.M. Revolution - Gundam SEED opening
Moment by Vivian or Kazuma - Gundam SEED opening
Anna ni issho datta no ni by See-Saw - Gundam SEED ending
OBSESSION by See-Saw - .hack//SIGN opening
Clover by Meg Rock - Solty Rei opening

I really like Colors of the Heart by UVERworld on Blood+ opening. I also like Lonely In Gorgeous-Tommy February6 on Paradise Kiss. Rurouni Kenshin has lotsa good songs too like It's Gonna Rain. Actually I hear most of J-pop from anime.

I've got so many! Well, here are a few i can remember

bleach - first opening (Asterisk - Orange Range)
air - opening (tori no uta) & ending
FLCL - ride on shooting star
Code geass - first opening
Ergo proxy - opening
Onegai teacher - opening
Higurashi no naku koro ni kai - opening
samurai champloo - opening

i know there are many more, but these just popped into my head.

hmmm never heard much but:

tokyo mew mew's english opening theme was cute i thought.
Dragonball gT's opening was cool and so was Digimon season 4's.
Yugiohs theme was also pretty cool..

Quote:

man, that's many

the ending of the anime kiddy grade (2002)
the opening of chrno crusade - something something pleasure line (2004)

the newer ones sucked. especially the endings of naruto and bleach

they hired that kind of wannabe bands who spoil the whole anime episode

Here's mine:

Bleach:
"Asterisk" - Orange Range (Opening)
"Thank You!!!" - Home Made Kazou (Ending)
"Life" - Yui (Ending)
My Pace (Ending)
Hanabi (Ending)
Shooting Star (Opening)

Pokemon:
Mezame Pokemon Master (Opening) - Rica's the best!!!

Lupin The Third:
Opening + Ending (from 1971)
Opening (Lupin The Third '78, and Lupin The Third '79)
"Love Theme" (instrumental + vocal version)(Ending)
"Love Squall" (Ending)
"Fairy Night" (Ending)

Dragonball Z:
"Cha-La-Head-Cha-La" (Opening)
1st Ending
"We Gotta Power" (Opening)
"Angel" ( 2nd Ending)

And the old anime from the 70's:
Mazinger Z (Opening)
Babei II (Opening)
Cutie Honey (Opening + Ending)
Candy Candy (Opening + Ending)
Majokko Megu Chan (Opening + Ending)
Makou no Makou Chan (Opening)

closing-any of school days (particularly 11th) they had like 8 closing songs and 12 episodes

Skeleton Liar for FLCL.

I actually went and saw a band that does Anime and videogame covers last weekend. They did a couple of songs by the Pillows, pretty sweet.