Pioneer used to dub most of the OP/ED to anime they released in NA up until they transitioned to DVD. I liked a lot of their dubbed songs; understanding the lyrics made you realize how hilariously awful most anisongs really are. Yeah, yeah the lyrics were often changed in translation, but come on most anisongs are bad.
Here's a few I liked:
I can't find the songs with the OP/ED animation, but here's Phantom Quest Corp. I think the songs are amazing, I'll let you guess whether they're amazing in a good or bad way.
Moldiver, another cheesy one. I liked the Japanese version better simply because yelling out ridiculous things like "Metamorforce!" is somehow less mortifying in Japanese:
Pretty Sammy OVA. The lyrics are incredibly inappropriate.
Tenchi Muyo OVA. I believe this is the same singer as the Pretty Sammy OVA above.
El Hazard The Wanderers OP
Now for an oddity. This is the opening from the Turbografx CD game The Dynastic Hero. I've always wondered what the story was behind this. The game came out about a half year after Pioneer started releasing Tenchi Muyo in English. This opening music sounds like something straight out of Tenchi. Makes me wonder if the same artists/studio that did the Tenchi songs also did this (the game has nothing to do with Tenchi).:
Record of Lodoss War OP. Again, I prefer the Japanese version, but the English is good too:
There's also another version of the Lodoss OP by Arai Akino (composed the OP). Slightly "Engrishy" but still interesting:
Record of Lodoss War ED
About Rayearth earlier in the thread, I liked Sandy Fox's songs for the English version, but I really liked one of the two English openings done by Working Designs for the Sega Saturn game. Unfortunately, the only video I could find on Youtube had horribly stuttering audio. I need to rip the opening and upload it to Youtube someday.
Also speaking of Sandy Fox, I have to admit I liked her version of "Freckles" for Rurouni Kenshin.
Now a Korean opening for Nurse Angel Ririka SOS. The Korean opening is very different from the Japanese one (the ED is similar to the Japanese ED):
Spanish opening for Maison Ikkoku. I think I'd love this song in any language.
I found a Catalan version too, if anyone know of other versions please post (I'd like to hear the song in French, but the French opening for Maison Ikkoku is a different song).