I dont know the order but.....
The first Shana OP
Black Rock Shooter
Tari Tari op
(dunno all the names sadly)

Xillia 2 OP

C3 OP

Guilty Crown OP

Haha my 3 top openings are all the nostalgic ones

1. bleach 1st op
2. inuyasha 1st op
3. death note 2nd op

My favourites are

1. Zoku Sayanara Zetsubou Sensei - Kuusou Rumba
2. Sacred Seven - stone cold
3. Robotics;notes - Junjou Spectra

1- Lilium (Elfen Lied)
2-Cruel Angels Thesis (NGE)
3 Tie between H.T.(Trigun) , We Are(One Piece op 1), We Go(One Piece op14) and Again (FMAB op1)

ya a 4 way tie, get over it.

I tend to fast forward through OPs, but there are a few cases where I like it so much that I don't do that even when I'm watching many episodes all in a row. Here are a few (it's not that much more than 3) that come immediately to mind.

Uragiri no Yuyake - Durarara!! (OP1; episodes 1-12)
Hero's Come Back!! - Naruto Shippuden (OP1; episodes 1-30)
One Reason - Deadman Wonderland
Disco Milk - Super Milk Chan

All of the openings and closings for Bakemonogatari and Nisemonogatari are pretty visually stunning of course but the songs aren't often to my taste. However, surprisingly (because it's got more of a frivolous pop sound than I usually like), there is one that sticks with me and fits comfortably on my list of favorites:

Platinum Disco - Nisemonogatari (episodes 8-10)

Honorable Mention--It's not an OP and I don't like the anime it's in (never could make it past the first episode or two), but that little folk song, "Toorimase" that is sung in Horizon in the Middle of Nowhere gets me every time and I could watch (and have) that part of episode 1 over and over again.

Fairytail - Towa no kizuna (op9)

Death note - The world (op1)

FMA - Cancion completa(op1)

1. Scandal - Harukaze (Bleach Op 15)

2. Idoling!!! - S.O.W. Sense of Wonder (Fairy Tail Op 2)

3. Do As Infinity - Kimi ga Inai Mirai (InuYasha: The Final Act Op)

1. colors of the heart- Blood+ (opening 3) http://www.youtube.com/watch?v=kDfm1gRIVBw
2. the light before we land- Gunslinger girl http://www.youtube.com/watch?v=xj3L_nduKdo
3. idea- Noein opening http://www.youtube.com/watch?v=FcTuQtlp5DY

1. Ghost in the Shell: Stand Alone Complex & 2nd Gig - Rise by Origa
https://www.youtube.com/watch?v=clddC-axybc

2.Kemono no Sou-ja Erin - Shizuku by Sukima Switch or Hajime Chitose
https://www.youtube.com/watch?v=9F9VYQdnX0c - Sukima Switch ver.
https://www.youtube.com/watch?v=ddENS-0QNCc - Hajime Chitose ver.

3. Utawarerumono - Musouka by Suara
https://www.youtube.com/watch?v=R7KMHqX1caw

Toradora Op 1 - Pre-Parade
http://www.youtube.com/watch?v=EAXwSiN0tto


Azumanaga Daioh - Soramimi Cake
http://www.youtube.com/watch?v=huWKSYUX5Fs


Nichijou OP2 - Hyadain no Joujou Yuujou
http://www.youtube.com/watch?v=-QdH0tKbc3Q

Madoka Magica: Connect
Baccano: Paradise lunch
GITS The Stand Alone Complex: Inner Universe

1. Re Sublimity - Kannazuki no Miko
2. What's up People?! - Death Note OP 2
3. Believe - Gundam SEED OP 3

My favorites would be:

1. Another OP Nightmare Contagion
2. Steins Gate OP Hacking to the Gate
3. No. 6 OP Spell

1) Tatami Galaxy
2) Cowboy Bebop
3) Serial Experiments Lain