Here are my favorites, but I warn you: I have a bunch of them, lol 😆 (although I have a pretty unique taste in intro songs, most of the time, so most people may not like, or wonder about, my choices 😛 ):
Yu Yu Hakusho opening - http://www.youtube.com/watch?v=8L-D6ZLwlCs
Outlaw Star opening - http://www.youtube.com/watch?v=R0N3L-pcGdc
Cowboy Bebop opening - http://www.youtube.com/watch?v=T6zDfxZ4NcE
Death Note 1st opening - http://www.youtube.com/watch?v=8R5Wagr-rc4
Death Note 2nd opening (and trust me when I say that I usually despise death metal under most circumstances, but this opening was very symbolic, and the music theme sort of grew on me after listening to it a few times) - http://www.youtube.com/watch?v=ZcJ1X12WsTA
Hunter X Hunter 2nd opening - http://www.youtube.com/watch?v=BFthlG2Qyns
D. Gray-Man 1st opening - http://www.youtube.com/watch?v=khhI2EdEbJE
D. Gray-Man 2nd opening - http://www.youtube.com/watch?v=khhI2EdEbJE
Rurouni Kenshin 1st opening - http://www.youtube.com/watch?v=kLJf_pnQl68
Bleach 1st opening - http://www.youtube.com/watch?v=JCjtl1_ECXA
Bleach 6th opening - http://www.youtube.com/watch?v=VN17C2J8lh0
Hikaru no Go 1st opening - http://www.youtube.com/watch?v=ASLWUSXAUwc
Hikaru no Go 2nd opening - http://www.youtube.com/watch?v=jtfFUMXu7kw
Black Lagoon opening - http://www.youtube.com/watch?v=Re8bIzbcu5w
Well, that's all....for now 😛....
Ensatsu got a lot of good ones, he even has the better of the yu yu openings.
I have to say, without a doubt, Karas is my favorite opening.
http://youtube.com/watch?v=YY2jZOXi51U
Then there are :
Keroro Gunsou
http://youtube.com/watch?v=RNbf-TATe14
King Gainer
http://youtube.com/watch?v=97j86qH91Nk
Kino
http://youtube.com/watch?v=tXDyyaMDIuQ
Jing
http://youtube.com/watch?v=frgkTRoRrAc
FMA
http://www.youtube.com/watch?v=rPOFASa7vNA
and the first Orphan opening, which I couldn't find a vid of yet.
There's more, but I'm not in the position to remember anything.
ensatsu-ken already posted the Cowboy bebop, Outlaw star, and Black lagoon intros.
as for the rest of my favorites
Claymore
http://youtube.com/watch?v=kZtZ9dNXtbg
Eureka seven
http://youtube.com/watch?v=-qb4SeMfSUM
http://youtube.com/watch?v=Zs2M2sAZpeU
Azumanga daioh
http://youtube.com/watch?v=huWKSYUX5Fs
Bleach
as much as I may dislike the series have to admit
the first intro kicked ass
http://youtube.com/watch?v=IdTNe2EPyZE
same goes for this particular Naruto intro
http://youtube.com/watch?v=mP91qkZFYqY
Orphen revenge
http://youtube.com/watch?v=dWJ3qU4kx5Y
hack//Roots: never seen the show but I like the intro
http://youtube.com/watch?v=hdOnvz5UMSo
.hack//sign: did watch it..it was alright
http://youtube.com/watch?v=1vIrnFhbzrI
Last Exile opening
http://youtube.com/watch?v=cBDK6wgmXqo
Cromartie High School
http://youtube.com/watch?v=fe7kMlgCqLw
Big O:
http://youtube.com/watch?v=AdA6iRk94Hc
http://youtube.com/watch?v=BsJj7qR6Djw
Samurai 7
http://youtube.com/watch?v=ba0ac9K3fSM
Elfen Lied: a lot of people seem to dislike this...probably the lack of J-POP
http://youtube.com/watch?v=hQ-CAB4vhpQ
I'm not done yet ..heh
Ghost in the shell
http://youtube.com/watch?v=f9uX6nt4g78
http://www.youtube.com/watch?v=I_7f_tv22VM&NR=1
serial experiments lain
http://www.youtube.com/watch?v=79MN_w0VMPE
Now and Then, Here and There Intro: pretty plain as far as intros goes..but It's probably one of my top 10. Great series as well.
http://www.youtube.com/watch?v=TGr74BEYqmo
Gungrave: **** YEAH!
http://youtube.com/watch?v=5J7hLdVshds
Baccano: **** YEAH!!
http://youtube.com/watch?v=oUjqlVt6y2A
Higurashi no Naku Koro ni: captures the mood of the show perfectly
http://youtube.com/watch?v=Cam6haL1HNM
second one not as much but still good
http://youtube.com/watch?v=4jFjUbE2cbk
Trigun
http://youtube.com/watch?v=KHW1nJUHxVM
One Piece - Brand New World
http://youtube.com/watch?v=KYwvmO16VxI
Pani Poni Dash 2 intro
http://youtube.com/watch?v=Y2scn9WUBOw
Hellsing: as much as the series may have sucked this intro probably holds the 1 spot in my favorites.
http://youtube.com/watch?v=hMNJwUUHMxc
Ergo Proxy
http://youtube.com/watch?v=4oT2W3gaUBc
Madlax: only anime to hold the title of "making me fall asleep mid episode on several occasions"
http://youtube.com/watch?v=z1eLIZ3l170
RahXephon
http://youtube.com/watch?v=rR-ZwXYkqzA
Fate Stay Night
http://youtube.com/watch?v=BUCwZkQHmVg
Bokurano op: only good part of the series..read the manga etc
http://youtube.com/watch?v=05p646nlYS0
Darker than black:
http://youtube.com/watch?v=6rv5hSt9oic
Excel Saga Opening
http://youtube.com/watch?v=K50l-9RNBo8
Vandread
http://youtube.com/watch?v=m917bshgmE0
http://youtube.com/watch?v=-sGJ4AEJo5k
Scryed
http://youtube.com/watch?v=JAC2j7bKsdE
haruhi op
http://youtube.com/watch?v=dTmwBsU32yE
Gurren Lagann
http://youtube.com/watch?v=7yCSHwQt1go
Shigurui 
http://youtube.com/watch?v=D0geiODQeyY
People, don't forget to either embed the Japanese opening in your post or post a link to it. That way, we can all see which opening you all are talking about. Almost every anime, if not all of them, have more than one Japanese opening and it would be nice if we knew which one that you liked.
Anyway, out of all the Japanese openings that I've seen, this would have to be my favorite. It's the opening to a series called "School Rumble: Term 2".
I might as well post my favorite opening.
This is the first opening for Naruto.
Both Venomous Yoshi and I embeded a video of our favorite opening in our post.
Great minds think alike. 😄
There.
YouTube video
this one for me:
YouTube video
i heat this song 😆
Originally posted by Blax_Hydralisk
This one:And this one: