However, various countries took the liberty of not dubbing the Japanese songs and instead creating their own "original" openings. I'll post some links to some of them, but feel free to add your own. If I had to rank them, they would be...
1) The opening for the Ocean dub of Dragon Ball. I gotta say, I think this song is pretty good. "Makafushigi Adventure" or a dub of it would have been better, but all things considered, this sets up the show pretty well and is one of the few good things to come out of FUNimation's first attempt at the show, in my opinion. The intro with the narrator sets up the more mysterious aspects of the show, and then we immediately dive into a very catchy, well-sung rock song with just the right amount of light-hearted cheesiness and enthusiasm. I don't love it, but I really like it!
2) "What Is Your Destiny," the Italian opening for DBZ. At times a little too reliant on techno...a lot of Italian anime openings seem to be like that, oddly enough...but I think it captures the adventurous spirit of the show, and they actually bothered to write lyrics. Whoever the singer is, you can tell he's really into what he's singing, and I find myself humming the song whenever I hear it. And hey, bonus point for taking a page out of Japan's book and sprinkling in a random English phrase throughout the song.

3) "Rock the Dragon," the North American opening for DBZ. To be honest, I've never really liked this song, and it doesn't really capture the tone or spirit of the show. It does, however, appear to have some energy behind it at least.
4) The Arabic opening (song name unknown). More "interesting" than good. Were it not for the visuals and repeated use of the words, "Dragon Ball," I'd have no reason to think this was an opening for DBZ. It sounds very ancient, mysterious, and Middle Eastern...interesting to listen to, but it doesn't particularly fit the show that it's being used to open, in my opinion.
5) "Rock the Dragon," the Westwood dub version. This is an alternative version of "Rock the Dragon" that was used to open the Westwood dub, a.k.a. the "post-Saban Ocean dub." I chuckle a little bit every time I hear this one. I'd normally put it at the same level as the original version, but the way the singer keeps extending "Zeeeeeeeeeeeeeeeee" always sounded silly to me. It sort of reminds me of that one adult we all knew who tried way too hard to sound cool to kids, and talked in odd ways that resembled "Macho Man" Randy Savage (RIP). "Seeeriously duuude, this is coooooolll.....oh yeeeeeaaaaahhhh!"
6) The French opening (song name unknown) for DBZ...this was also dubbed into a few different languages in European countries that received the French version of the show for dubbing purposes. Oh boy...this one is just torture to listen to, I'm sad to say. The Westwood version of "Rock the Dragon" at least had some decent guitar and drumwork here and there. With this opening, we have nothing but cheap-sounding synthesizers, extremely repetitive vocals, and an overall sound that sounds far, far too childish, even for a kid's show.
Which one is your favorite (if you like them at all, of course, and why)? Do you have any other "original" international openings you'd like to share?