fluffybacon:
Why does this only have to apply to anime? Are all the other mediums of motion picture not good enough for you?

Anime tends to have more comprehensive openings and opening themes than a lot of other TV shows, or at least that's my best guess.

I don't feel like posting videos or links because I'm really damn lazy. If you're truly interested in some of these, I have the feeling you'll be willing to put forth more effort in looking these up.

R.O.D. the TV Series (Think Coyboy Bebop with more imagry and intensity)
Ah, My Goddess Second Season (Gotta love the Bagpipes)
Lucky Star (DANCING CHIBIS!!!)

1. Cowboy Bebop
2. Elfen Lied
3. Azumanga Daioh.

Yes! The weirdest combo possible! I love the music in the first 2, the imagery in the 2nd, and Azumanga's is so endearing and silly. It fits the show well.

In no particular order.

Negima!?, Bleach Opening 12, or Neon Genesis Evangelion OP

I'll to the best 3 of all time!!

http://www.youtube.com/watch?v=EqEYuzD5RcE

http://www.youtube.com/watch?v=wAn6So9tURU

http://www.youtube.com/watch?v=L6gaeJkLNWE

Not really an anime, but it's awesome and it took me forever to find the american version of the opening (the japanese version has lyrics which fuck it up big time) so I'm posting it anyways...that and I can't think of any anime openings I like

Azraellod:

Higurashi no Naku Koro ni Kai

Ciarang:

Higurashi No Naku Koro Ni

I love you two.
and that is 2 out of 3 for my favourite openings.
I suppose this will be my third one

Ghost in The Shell 2:Innocence.
Neon Genesis Evangelion.
Higurashi No Naku Koro Ni.

For my money:

Tales of the Abyss: http://www.youtube.com/watch?v=ybTnCcrZsMk

That opening convinced me to buy the game, it's that good.

Full Metal Panic: http://www.youtube.com/watch?v=a6E6XH51wJA

http://www.youtube.com/watch?v=Qy_oppK6DAo

http://www.youtube.com/watch?v=xf8R0IEm-8Y

I'm rolling all three together because it's one of my favorite series, and if I could have populated this list with just those three openings. Seriously, watch it, you won't regret it.

Serial Experiments Lain: http://www.youtube.com/watch?v=thY2y-NoGjc&feature=related

Fantastic song, beautifully performed, and the opening does nothing to set you up for the mind-rape that's to come.

And, of course, I'd be remiss not to mention the opening from Paprika: http://www.youtube.com/watch?v=xqg3Sw3s9Wg

Yeah, that ended up more like a top six... Don't judge me

#1: Azumanga Daioh/all the Minami-ke ones
#2: Seto no Hanayome...Slash...Nyan Koi!...Slash...K-on!...Slash...Lucky Star...Slash...Haruhi...
#3: The second OP for the first Season of Sayonara Zetsubou Sensei( And all of the EDs for it)
Sorry that there's 7 listed down there. :P Would've listed Haruhi and Azumanga Daioh, but I figured seven was enough...

I totally forgot:

Happy Lesson:

http://www.youtube.com/watch?v=u5ah14f_yPM

http://www.youtube.com/watch?v=TMB6QcXq07s

Here goes:

1. Clannad (1st OP: Megumeru) - Love this one because 1) the show evokes such an insane amount of emotion that it's impossible not to love this opening, 2) I adore the song, and 3) the amount of foreshadowing, even to events in the second season of the show, is astronomical. Clannad is guaranteed to make you fall in love with the characters, and will probably make you cry at least once, no matter how tough you are.

2. Death Note (1st OP: The WORLD) - Because of the sheer amount of symbolism contained in it, and just for having an awesome song that got my blood pumping before every episode.

3. Naruto Shippuuden (Blue Bird) - Because the show is always packed with emotion, so the songs often bear and reflect that. This amazing song is no exception, with one of the series' better opening videos to accompany it.

And... screw it, I have to include them!!!

4. Full Metal Alchemist (1st OP: Melissa) - Just... great song. And the video is fantastic, pairing perfectly with the early events of the show.

5. Darker Than Black: Gemini of the Meteor (Tsukiakari no Michishirube) - Great song, great video. I really don't know what else to say. Watch Darker Than Black, then partake in this excellent sequel season.

6. Digimon Tamers (The Biggest Dreamer) - Same reasons. Love the song, love the video, foreshadowing is fantastic, etc. Amazing show: it was season 3 of Digimon.

I know I went way over 3, but I couldn't bear only listing three of these... and I even left out Haruka Kanata and Tori no Uta... :(

1. Renai Circulation - Bakemonogatari
2. New World - .hack//DUSK
3. Cagayake! Girls - K-ON!

And I suppose:

3 Saber Marionette J Opening
2 Escaflowne
1 Ghost in the Shell: SAC (Yes, I know. Hoooow original but still!)

Mine would be as followed...

To name a few. I have admittedly played both Higurashi themes in extreme excess; the first over two hundred times in under a week.

Suiseiseki IRL:

Desert Punk 2nd OP

Rozen Maiden (season 1)

Kodomo no Jikan 2nd term

Sigh, I have come to the conclusion Rozen Maiden's theme is quite addictive and to which I cast blame on you. :P

These are my favourites:

Rurouni Kenshin (the first opening)
Blood + (the third opening - Colours of the Heart)
Ghost in the Shell: SAC (first season)

hmmm... .hack//roots takes first for me followed by .hack//sign and coming in third is DNangels

A random person:

fluffybacon:
Why does this only have to apply to anime? Are all the other mediums of motion picture not good enough for you?

Anime tends to have more comprehensive openings and opening themes than a lot of other TV shows, or at least that's my best guess.

Well, I don't mind some show "openings", like House, but as I do with anime OPs, I tend to skip them.

fluffybacon:
Why does this only have to apply to anime? Are all the other mediums of motion picture not good enough for you?

You came across quite rude there. However I do enjoy other shows besides anime, like Scrubs, Doctor Who or Heroes just to name a few. However if it bothers you that much, then feel free to post a non-anime opening that you like. (If you want to that is)

#1: Neon Genesis Evangelion
#2: Baccano!
#3: Darker Than Black op.2.

Del-Toro:
The First opening of Gundam 0083: Stardust Memory, the tune isn't bad either.
-schipp -

Without a doubt the best Gundam opening.

The music alone won't sell these or anything, but the opening sequences to JoJo's Bizarre Adventure are pretty great. Here's the first one:

http://www.youtube.com/watch?v=Vhz3WJrhSHM

I couldn't find any of the openings separated from the rest of their episodes, so it's just the first part of the first episode.

fluffybacon:
Why does this only have to apply to anime? Are all the other mediums of motion picture not good enough for you?

http://tvtropes.org/pmwiki/pmwiki.php/Main/AnimeThemeSong

EDIT:Fixed, and thank you, A random person.

Well, being a major anime buff... i would have to say...

#1: D Gray man opening #4: It was good, had enough action not to give too much of the story away, and it looked pretty awesome.
#2: Black Lagoon Opening: What can i say, it's Black Lagoon, of course its on the list.
#3: Cowboy Bebop: Reminded me a little of a James Bond style theme.

other worhty mentions are: Busou Renkin, Death Note OP#1, Gundam 00 first season #1, GUndam 00 s2 #2, Gundam seed Op#1, Neon Genesis, Claymore, and Fafner in the Azure.

These two are the only ones I really liked. I usually find anime openings too annoying.

Knonsense:
The music alone won't sell these or anything, but the opening sequences to JoJo's Bizarre Adventure are pretty great. Here's the first one:

http://www.youtube.com/watch?v=Vhz3WJrhSHM

I couldn't find any of the openings separated from the rest of their episodes, so it's just the first part of the first episode.

A random person:

Why does this only have to apply to anime? Are all the other mediums of motion picture not good enough for you?

http://tvtropes.org/pmwiki/pmwiki.php/Main/AnimeThemeSong

I think your quoting screwed up, I was responding to someone who said that.

But yes, that TV Tropes link is an appropriate response.

Ugh, this won't be easy as I have quite many favourites...well, here goes, my top three openings:

I quite liked Code Geass, 2nd opening: http://www.youtube.com/watch?v=Se6wBWb-M20&feature=related

Hunter x Hunter, first opening...but I just can't find the video and the music together anywhere. Anybody know where can I find it?

Heroic Age, it's so badass: http://www.youtube.com/watch?v=l09yFzAKN6k

You have no idea how hard it was to choose these, it took me about half an hour...anyway, these are by no means my only favourites, but I wanted to go by this threads rules.