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.

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 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 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.