I've been waiting until I had some free time to devote to this thread, since I have many favorites!
OPs:
Tenchi Muyo Ryo-Ohki
I love this song, it's so weird and mysterious. This opening is classy and subtle and not overdone. I also like some other Tenchi Muyo openings, like
Pioneer (although the animation for that one kinda sucks, the song is great) and
Dream Away.
Macross 2: Hush of a Million Years
This might be more nostalgia than anything. Macross 2 coming out may as well have been the return of God as far as I was concerned. Little did I know back then that it would be relegated to non-canon status after Macross Plus and Macross 7 came out. Still a cool song with cool animation.
Anything from
Robot Anime History 1984-1984 is awesome - seriously, watch the whole damn thing (maybe skip God Mazinger). Awesome songs with great animation.
I also like all the American intros mentioned in my post
here.
EDs:
Lodoss Wars: Fantasia of the Wind
Amazing song. Has hints of What a Feeling from the FlashDance movie. Features what sounds like traditional Japanese instruments (at least to my gaijin ears). Also look at those bad-ass fantasy stills! Unicorns and Dragons, oh my! I always wondered why everyone loves Adèsso e Fortuna when this song is so much cooler.
Macross 7 : My Friends
Rocking song, but also really pretty. Love it. Also beautiful artwork by Haruhiko Mikimoto. What's not to like?
Tenchi Muyo: Talent for Love
I feel seriously heavy nostalgia when I watch this. Tenchi Muyo was the second anime I fell in love with after Robotech. The song is fun and catchy and the animation is pretty cute. Gotta love that little cabbit!
BONUS:
I love
Full Moon Light from Devil Hunter Yohko. It was like a bonus music video, not an OP or ED. The song is sickeningly sweet and super poppy.