Another anime, and a certified classic at that;
Dragon Half. I watched it years ago for the first time, watched it again a few times over the years and recently re-watched it with a friend of mine.
Dragon Half tells the story of Mink, the daughter of a dragon and a retired dragon slayer (don't ask)
So, what would you do when you're a pretty girl with little dragon horns, a dragon's tail and dragon wings, and hot for idol singer (and dragon slayer) Dick Saucer? You set on a quest to visit his concert, naturally.
Unfortunately there are some people who, for one reason or the other, are trying to get their hands on Mink; the King (in order to get to her mother, who he wants to marry) and his henchmen, and the King's daughter, who is a slime half, and wants to get rid of Mink to have Dick Saucer all to herself.
The two-part OVA is packed with small jokes and is set in a realm of dragons and knights, with a hint of 1993-technology mixed in.
The real kicker comes at the end of each episode, where Mink sings the ending: "Watashi no Tamagoyaki", or "My Omelette" for those of you who do not speak Japanese. The lyrics are too crazy to quote here, so I'd recommend you go and watch it. :)
Cheers, K.