For opening song: Cha-la-head cha-la (Dragonball Z)
-This opening just is an istant classic and easily is a great opening. It's so perfectly made in sync with the song, and its just freakin sweet.
For ending song: Wonderful Life (Planetes)
-There are better ending songs, but when I first watched planetes this ending song instantly became a fav in my book. But, there are betters.
Evangelion's OP always get's me pumped up, but for me the best opening in anime is "Koi da Panic" from the Ranma 1/2 OVA's, reason why, I just like the style of 90's pop music, plus it's fun to play at a party, and also "Get Along" from Slayers (but that's just because I'm a Megumi Hayashibara nut)
As for ending songs: I like "Junk Boy" from MAZE: The Megaburst Space, I just love it, it's just crazy and fun, and also "Sleepless Angels" from ZENKI, after I heard this I instantly got addicted to this song
The Queen-inspired opening from Big O has always been one of my favorites. Just Communication from Gundam Wing is also up there for me. And We Are from One Piece.
Outlaw Star's got a groovy OP and beautiful ERAB. I like the ED from Angel Links too, but the show itself is not as good as OS.
Any that Yoko Kanno worked on.
Paranoia Agent not only has great OP and ED songs, but awesome sequences for them.
I can't listen to Dream Island without thinking of the characters laughing while the world goes to hell.
Death Note's second OP, What's Up People?!
Excel Saga's OP and ED are hilarious!
Samurai Champloo's OP and all the different ED songs.
Bobobo's 2nd OP, Baka Survivor.
Big O's original OP song was great too. It's a real shame it was replaced by a different OP which I don't really like all that much.
I also liked the 2nd and 3rd OPs for Blood+.
Rurouni Kenshin's 3rd ED, Heart of the Sword.
I hate to admit this, but I actually sang along with Reel Big Fish's OP for Rave Master a few times (seeking out the stones with a carrot-nosed dog?!).