Well I'm watching Parasyte: Kiseijuu Sei no kakuritsu and the opening is super awesome... I'm really liking that kind of Japanese music.
There is a lot of nice anime openings, so, what are your favorites?

My favorite is Death Note but that is probably because Death Note is my favorite anime of all time. :3

I have quite a few. The one for Saint Seiya: The Lost Canvas is very good, as are the Dragon Ball Z ones.

I also hold in high regards the first opening of Cardfight!! Vanguard, and the last two Japanese openings for Yu-Gi-Oh! 5D's.

Still, I think I'm missing some, but out of the top of my head, these are my favorites

Ugh, so many... FMA: Brotherhood Opening, Great Teacher Onizuka Ending, Wolf's Rain Ending, Naruto Opening (Go!!!), Gungrave Ending, As***eruze Baby Opening and Ending (Both are in my top 10 favorite anime opening/endings), E's Otherwise Opening (Another of my favorites), Avenger Opening and Ending, Gunslinger Girl Opening, Black Lagoon Opening (I know it's Engrish, but it fits. XD) BLEACH (Change and Ichirin no Hana) Blue Seed Opening and Ending, Ushio and Tora Opening and Ending (It's a pretty obscure anime, but it's a good one) Rurouni Kenshin Opening and Ending (Heart of Sword is one of my all time favorites) Ghost in the Shell Stand Alone Complex both Opening and Endings, Turn A Gundam second Ending (another favorite), Gundam X Opening, Gundam 00 Opening and Endings, Sakura Wars (Geki! Teikoku), Samurai Champloo Ending, etc...  ... Like, seriously... I could keep going... But I'll stop... But I really could.

dovakhiin97 : I particularly like Death Note (Well... maybe because I've read all 13 volumes and watched all thirty-seven episodes)
And Full Metal Alchemist Brotherhood Opening three (Wow.. What a long name).
   

I have a lot of favorite's but I will only list a few.

1) Black Bullet Opening 2, the full version is even better and the animation is awesome.

2) Deadman Wonderland opening, the full version is epic.

3) Naruto Shippuden opening 4, I don't really like the full version so I prefer the TV size.

4) Naruto Shippuden opening 5, I love the lyric's.

5) Attack on Titan Opening 1, one of the most dramatic opening I have seen.

6) My Teen Romantic Comedy SNAFU opening 2, I love listening to this on the speakers of my radio.

7) Sora no Otoshimono opening, cute animation and cool beat.

8) .hack//Root's Opening, an old favorite of mine.

9) .hack//Sign Opening, the opening is just weird .. but that beat I just can't resist. 

10) Gravitation Opening, I listen to this one so much that I actually memorized the lyric's.

11) Ghost in the Shell Stand Alone Complex opening, the TV size and Full Version are beautiful.

Hard to pick a favorite because most one's I've seen are good...hmm...how about the Bleach opening during the Espada Arc? Not to mention the Fullmetal Alchemist opening, Black Butler, Another, and definitely Blood + and Blood-C.

Probably would've listed at least 20+ more if I could remember, but just being lazy and sharing this:

DAICON IV, unsure if it counts, but still certainly my favorite OP in recent memory.
Old school anime production, no computers, made in one of the teams house and garage.
Pure 80's culture, and set to a backgrop of music from 70's pop band ELO.

All your replies makes me feel like a super newbie in the animes.

Lets see....

sailor moon
ultimate muscle
card captors
tecknoman
digimon season 1-3
pokemon old versions
Battle B-dman
once piece 4kids version don't care what people say about that
yu--gi oh old school ones
beyblade old school
duel masters
flame of recca
naruto and some from shippuden
etc

dovakhiin97 : I am split between two...
Unravel from Tokyo Ghoul
Hacking into the Gate from Stiensgate... 

My favorite opening is the one for Persona 4 The Animation, I love it because the art style is pretty cool and the music is amazing, not just for that but for the whole P4 series as well. I also love the Japanese version of the Pokemon XY anime opening.

My favorite is probably Death Note, but I'd say Dragon Ball Z is a close second simply because DBZ is my favorite anime.

My favorite would probably be the first opening theme in Attack on Titan. That theme is easily the best song I've ever heard in anime.

Chihayafuru has a nice relaxing intro but death note is my personal favourite intro :p

I have too many favorites, but you can bet your bottom I have a few from Naruto and Naruto Shippuden.
Off the top of my head, "Yura Yura" by Hearts Grow and "U can do it!" by Domino.
Kuroko's Basket Season 1 Opening 1 - "Can Do" by GRANRODEO 
Kuroko's Basket Season 2 Opening 2 - "The Other Self" by GRANRODEO
Attack on Titan Season 1 Opening 1 - "Guren no Yumiya/The Crimson Bow and Arrow" by Linked Horizon
Tokyo Ghoul Season 1 Opening 1 - "Unravel" by TK from Ling Tos***e Sigure
Ergo Proxy Opening 1 - "Kiri" by MONORAL

Cowboy Bebop has the best opening hands down

There are just too many to have a favorite.  That's like asking who my favorite band is, or my favorite style of music.  First off, I will list the Dragon Ball Z openers, save for the GT series.  Rosario Vampire Capu 2 was a great discotheque as well as a good show.  Sekirei and it's second season Pure Engagement is one of my favorite anime and both openings are wonderful.  I love the opening to Claymore.  Maburaho is great.  Asu no Yoichi is wonderful.  Ikki Tousen - Xtreme Xecutor was awesome.  DearS was good.  A few more, I promise.  Dakara Boku wa H Ga Dekinai and last but not least To Love Ru Darkness.  Both were great, and all these shows were wonderful.

The opening of Dragon Ball Z Kai is great to me, and the intros for all 3 seasons of RWBY. I am currently watching The Asterisk War, which has a decent intro, but nothing to get excited about.